Mathematics › Applied Mathematics

Holomorphic and Operator Theory

Works Count: 39584

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This cluster of papers covers a wide range of topics in complex analysis and operator theory, including composition operators, weighted spaces, Toeplitz operators, hypercyclic operators, Bergman spaces, holomorphic functions, Nevanlinna–Pick kernels, operator theory, function theory, and spectral factorization.

Keywords

Composition Operators; Weighted Spaces; Toeplitz Operators; Hypercyclic Operators; Bergman Spaces; Holomorphic Functions; Nevanlinna–Pick Kernels; Operator Theory; Function Theory; Spectral Factorization

Operator theory in function spaces

1991-07-01

Kehe Zhu

Notions of Convexity

2007-01-01

Lars Hörmander

The first two chapters of the book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the … The first two chapters of the book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions, pseudoconvex sets and sets which are convex for supports or singular supports with respect to a differential operator. In addition the convexity conditions which are relevant for local or global existence of holomorphic solutions of holomorphic differential equations are discussed, leading up to Trepreau's theorem on sufficiency of condition (psi) for microlocal solvability in the analytic category.

Pseudo-Hermitian structures on a real hypersurface

1978-01-01

S. M. Webster

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Partial Differential Equations in Several Complex Variables

2001-11-15

So-Chin Chen , Mei-Chi Shaw

This book is intended as both an introductory text and a reference book for those interested in studying several complex variables in the context of partial differential equations. In the … This book is intended as both an introductory text and a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the study of Cauchy-Riemann and tangential Cauchy-Riemann operators; this progress greatly influenced the development of PDEs and several complex variables. After the background material in complex analysis is developed in Chapters 1 to 3, the next three chapters are devoted to the solvability and regularity of the Cauchy-Riemann equations using Hilbert space techniques. The authors provide a systematic study of the Cauchy-Riemann equations and the \bar\partial-Neumann problem, including Hormander's L2 existence progress on the global regularity and irregularity of the \bar\partial-Neumann operators. The second part of the book gives a comprehensive study of the tangential Cauchy-Riemann equations, another important class of equations in several complex variables first studied by Lewy. An up-to-date account of the L2 theory for \bar\partial_b operator is given. Explicit integral solution representations are constructed both on the Heisenberg groups and on strictly convex boundaries with estimates in Holder and L2 spaces. Embeddability of abstract CR structures is discussed in detail here for the first time. Titles in this series are co-published with International Press, Cambridge, MA.

Weighted Norm Inequalities and Related Topics

1985-01-01

José Garcı́a-Cuerva , J.-L. Rubio de Francia

A Primer on Spectral Theory

1991-01-01

Bernard Aupetit

Commutation Properties of Hilbert Space Operators and Related Topics

1967-01-01

C. R. Putnam

Theory and Applications of Volterra Operators in Hilbert Space

2004-06-16

Israel Gohberg , M. Г. Крейн

Hankel Operators and Their Applications

2003-01-01

Vladimir Peller

Operateurs Maximaux Monotones - Et Semi-Groupes De Contractions Dans Les Espaces De Hilbert

1973-01-01

Haïm Brézis

The spectral theory of Toeplitz operators

1981-01-01

L. Boutet de Monvel , Victor Guillemin

The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous … The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations.If P is a self-adjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known that the asymptotic behavior of its eigenvalues is closely related to the behavior of the bicharacteristic flow generated by its symbol.It is natural to ask if similar results are true for Toeplitz operators. In the course of answering this question, the authors explore in depth the analogies between Toeplitz operators and pseudodifferential operators and show that both can be viewed as the quantized objects associated with functions on compact contact manifolds.

The Functional Calculus for Sectorial Operators

2006-01-01

Markus Haase

In Section 2.1 the basic theory of sectorial operators is developed, including examples and the concept of sectorial approximation. In Section 2.2 we introduce some notation for certain spaces of … In Section 2.1 the basic theory of sectorial operators is developed, including examples and the concept of sectorial approximation. In Section 2.2 we introduce some notation for certain spaces of holomorphic functions on sectors. A functional calculus for sectorial operators is constructed in Section 2.3 along the lines of the abstract framework of Chapter 1. Fundamental properties like the composition rule are proved. In Section 2.5 we give natural extensions of the functional calculus to larger function spaces in the case where the given operator is bounded and/or invertible. In this way a panorama of functional calculi is developed. In Section 2.6 some mixed topics are discussed, e.g., adjoints and restrictions of sectorial operators and some fundamental boundedness and some first approximation results. Section 2.7 contains a spectral mapping theorem.

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The Classical Moment Problem.

1968-01-01

Stephen Hoffman , Н. И. Ахиезер

Quasiconformally homogeneous domains

1976-12-01

F. W. Gehring , Bruce Palka

The Essential Norm of a Composition Operator

1987-03-01

Joel H. Shapiro

Universal families and hypercyclic operators

1999-06-23

Karl-Goswin Grosse-Erdmann

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C∗-algebras associated with irrational rotations

1981-04-01

Marc A. Rieffel

For any irrational number a let Aa be the transformation group C*-algebra for the action of the integers on the circle by powers of the rotation by angle 2πa. It … For any irrational number a let Aa be the transformation group C*-algebra for the action of the integers on the circle by powers of the rotation by angle 2πa. It is known that Aa is simple and has a unique normalized trace, τ. We show that for every β in (Z + Za) Π [0,1] there is a projection p in Aa with τ(p) = β. When this fact is combined with the very recent result of Pimsner and Voiculescu that if p is any projection in Aa then τ{p) must be in the above set, one can immediately show that, except for some obvious redundancies, the Aa are not isomorphic for different a. Moreover, we show that Aa and Aβ are strongly Morita equivalent exactly if a and β are in the same orbit under the action of GL (2, Z) on irrational numbers. 0* Introduction* Let a be an irrational number, and let S

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Algebraic Properties of Toeplitz operators.

1964-01-01

Paul R. Halmos , Arlen Brown

A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines

1970-04-01

George Kimeldorf , Grace Wahba

Abstract : The report presents classes of prior distributions for which the Bayes' estimate of an unknown function given certain observations is a spline function. (Author) Abstract : The report presents classes of prior distributions for which the Bayes' estimate of an unknown function given certain observations is a spline function. (Author)

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Generalizeds-numbers ofτ-measurable operators

1986-06-01

Thierry Fack , Hideki Kosaki

We give a self-contained exposition on generalized s-numbers of τ-nieasurable operators affiliated with a semi-finite von Neumann algebra.As applications, dominated convergence theorems for a gage and convexity (or concavity) inequalities … We give a self-contained exposition on generalized s-numbers of τ-nieasurable operators affiliated with a semi-finite von Neumann algebra.As applications, dominated convergence theorems for a gage and convexity (or concavity) inequalities are investigated.In particular, relation between the classical //-norm inequalities and inequalities involving generalized s-numbers due to A. Grothendieck, J. von Neumann, H. Weyl and the first named author is clarified.Also, the Haagerup L pspaces (associated with a general von Neumann algebra) are considered.Haagerup L^-spaces "from scratch."Proofs are known, but it may not be without interest.In fact, some false proofs exist in the literature.This work was completed during a stay of the first named author at the Mathematical Sciences Research Institute of Berkeley.The author is grateful to the Institute for its warm hospitality

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A joint spectrum for several commuting operators

1970-10-01

Joseph L. Taylor

Estimates for translation invariant operators in Lp spaces

1960-01-01

Lars Hörmander

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Ten problems in Hilbert space

1970-09-01

Paul R. Halmos

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A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces

1983-12-01

Wilhelm Kaup

The uncertainty principle

1983-01-01

Charles Fefferman

On considere l'existence et la regularite des solutions d'equations aux derivees partielles, la construction de solutions fondamentales explicites et les valeurs propres d'operateurs de Schrodinger On considere l'existence et la regularite des solutions d'equations aux derivees partielles, la construction de solutions fondamentales explicites et les valeurs propres d'operateurs de Schrodinger

Interpolations by Bounded Analytic Functions and the Corona Problem

1962-11-01

Lennart Carleson

On subharmonic functions and differential geometry in the large

1958-12-01

Alfréd Huber

Complex symmetric operators and applications

2005-05-26

Stephan Ramon Garcia , Mihai Putinar

We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable … We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, self-adjoint extensions of symmetric operators, rank-one unitary perturbations of the compressed shift, Darlington synthesis and matrix-valued inner functions, and free bounded analytic interpolation in the disk.

Determinants of Cauchy-Riemann operators over a Riemann surface

1985-01-01

Daniel Quillen

Operators with dense, invariant, cyclic vector manifolds

1991-06-01

Gilles Godefroy , Joel H. Shapiro

Analysis of Toeplitz Operators

1990-01-01

Albrecht Böttcher , Bernd Silbermann

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An Interpolation Problem for Bounded Analytic Functions

1958-10-01

Lennart Carleson

be possible for a given sequence of points {zv}, I z, 1, and an analytic function f(z) in I z i < 1, I f(z) I _ 1. The result … be possible for a given sequence of points {zv}, I z, 1, and an analytic function f(z) in I z i < 1, I f(z) I _ 1. The result is, however, very implicit ancd gives in a concrete situation very little help in deciding if the interpolatioln is possible or not. The object of the present paper is to give a simple and explicit condition on {z,} under which the interpolation (1. 1) is possible with a bounded function f(z). If we allow {w,} to be an arbitrary bounded sequence, the condition is also a necessary one. It should be observed that even the existence of any infinite such sequence {zv} is non-trivial; this problem was suggested by R. C. Buck and constructions of such examples have also recentlybeen given by G-leason and Newman (unpublished). The proof of the main theorem depends on a reformulation of problem (1.1) which is presented in section 2. It is essentially included in a result by Garabedian [2]; since the discussion there is quite general and the proof complicated, we have included a complete and simple proof here. Section 3 contains an inequality of the Schwarz type, which is the crucial step in our proof. This is then completed in section 4. The last section is devoted to an application to the ideal structure in the algebra of bounded analytic functions.

The Bergman kernel and biholomorphic mappings of pseudoconvex domains

1974-03-01

Charles Fefferman

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Complex Analytic Coordinates in Almost Complex Manifolds

1957-05-01

August Newlander , Louis Nirenberg

A manifold is called a complex manifold if it can be covered by coordinate patches with complex coordinates in which the coordinates in overlapping patches are related by complex analytic … A manifold is called a complex manifold if it can be covered by coordinate patches with complex coordinates in which the coordinates in overlapping patches are related by complex analytic transformations. On such a manifold scalar multiplication by i in the tangent space has an invariant meaning. An even dimensional 2n real manifold is called almost complex if there is a linear transformation J defined on the tangent space at every point (and varying differentiably with respect to local coordinates) whose square is minus the identity, i.e. if there is a real tensor field h' satisfying

Theory of Bergman Spaces

2000-01-01

Håakan Hedenmalm , Boris Korenblum , Kehe Zhu

On the extension ofL 2 holomorphic functions

1987-06-01

Takeo Ohsawa , Kenshô Takegoshi

Weighted Norm Inequalities for the Hardy Maximal Function

1972-03-01

Benjamin Muckenhoupt

The principal problem considered is the determination of all nonnegative functions, $U(x)$, for which there is a constant, C, such that \[ \int _J {{{[{f^ \ast }(x)]}^p}U(x)dx \leqq C\int _J … The principal problem considered is the determination of all nonnegative functions, $U(x)$, for which there is a constant, C, such that \[ \int _J {{{[{f^ \ast }(x)]}^p}U(x)dx \leqq C\int _J {|f(x){|^p}U(x)dx,} } \] where $1 < p < \infty$, J is a fixed interval, C is independent of f, and ${f^ \ast }$ is the Hardy maximal function, \[ {f^ \ast }(x) = \sup \limits _{y \ne x;y \in J} \frac {1}{{y - x}}\int _x^y {|f(t)|dt.} \] The main result is that $U(x)$ is such a function if and only if \[ \left [ {\int _I {U(x)dx} } \right ]{\left [ {\int _I {{{[U(x)]}^{ - 1/(p - 1)}}dx} } \right ]^{p - 1}} \leqq K|I{|^p}\] where I is any subinterval of J, $|I|$ denotes the length of I and K is a constant independent of I. Various related problems are also considered. These include weak type results, the problem when there are different weight functions on the two sides of the inequality, the case when $p = 1$ or $p = \infty$, a weighted definition of the maximal function, and the result in higher dimensions. Applications of the results to mean summability of Fourier and Gegenbauer series are also given.

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Analyse Harmonique Non-Commutative sur Certains Espaces Homogenes

1971-01-01

Ronald R. Coifman , Guido Weiss

Spaces of Holomorphic Functions in the Unit Ball

2005-01-01

Kehe Zhu

The Bergman–Fridman invariant on some classes of pseudoconvex domains

2025-06-25

Rahul Kumar , Prachi Mahajan | Proceedings - Mathematical Sciences

Operator relations characterizing higher-order differential operators

2025-06-25

Włodzimierz Fechner , Eszter Gselmann , Aleksandra Świątczak | Acta Mathematica Academiae Scientiarum Hungaricae

Mean Ergodicity of Multiplication Operators in Weighted Dirichlet Spaces

2025-06-25

A. Bonilla , Daniel Seco | Results in Mathematics

On Dirichlet-type and n-isometric shifts in finite rank de Branges-Rovnyak spaces

2025-06-23

Shuaibing Luo , Eskil Rydhe | Science China Mathematics

Positive self-commutators of positive operators

2025-06-21

Roman Drnovšek , Marko Kandić | Positivity

Abstract We consider a positive operator A on a Hilbert lattice such that its self-commutator $$C = A^* A - A A^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>A</mml:mi> <mml:mo>∗</mml:mo> … Abstract We consider a positive operator A on a Hilbert lattice such that its self-commutator $$C = A^* A - A A^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>A</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mi>A</mml:mi> <mml:mo>-</mml:mo> <mml:mi>A</mml:mi> <mml:msup> <mml:mi>A</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:math> is positive. If A is also idempotent, then it is an orthogonal projection, and so $$C = 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . Similarly, if A is power compact, then $$C = 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> as well. We prove that every positive compact central operator on a separable infinite-dimensional Hilbert lattice $$\mathcal H$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>H</mml:mi> </mml:math> is a self-commutator of a positive operator. We also show that every positive central operator on $$\mathcal H$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>H</mml:mi> </mml:math> is a sum of two positive self-commutators of positive operators.

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On the Relation Between Distances and Seminorms on Fréchet Spaces, with Application to Isometries

2025-06-20

Isabelle Chalendar , Lucas Oger , J. R. Partington | Mathematics

A study is made of linear isometries on Fréchet spaces for which the metric is given in terms of a sequence of seminorms. This establishes sufficient conditions on the growth … A study is made of linear isometries on Fréchet spaces for which the metric is given in terms of a sequence of seminorms. This establishes sufficient conditions on the growth of the function that defines the metric in terms of the seminorms to ensure that a linear operator preserving the metric also preserves each of these seminorms. As an application, characterizations are given of the isometries on various spaces including those of holomorphic functions on complex domains and continuous functions on open sets, extending the Banach–Stone theorem to surjective and nonsurjective cases.

On some conditions for the existence of a holomorphic continuation of functions in a ball

2025-06-20

А. М. Кытманов , S. G. Myslivets | Vestnik Udmurtskogo Universiteta Matematika Mekhanika Komp yuternye Nauki

The paper considers the Cauchy–Fantappiè integral representation, which is close to the Bochner–Martinelli integral representation, and the kernel of which consists of derivatives of the fundamental solution of the Laplace … The paper considers the Cauchy–Fantappiè integral representation, which is close to the Bochner–Martinelli integral representation, and the kernel of which consists of derivatives of the fundamental solution of the Laplace equation. The aim of the work is to study the properties of this integral representation for integrable functions. Namely, the paper considers an integral (integral operator) with this kernel for integrable functions $f$ on the boundary $S$ of the unit ball $B$. Iterations of the integral of this integral operator of the order $k$ are considered. We prove that they converge to a function holomorphic in $B$ as $k\to\infty$.

p-Hankel matrices on Dirichlet-type spaces

2025-06-20

Xiaofen Lv , Wang Lei , Xiaomin Tang | Banach Journal of Mathematical Analysis

Asymptotic behaviour of the Bergman invariant and Kobayashi metric on exponentially flat infinite type domains

2025-06-19

Ravi Shankar Jaiswal | Complex Analysis and its Synergies

Abstract We prove the nontangential asymptotic limits of the Bergman canonical invariant, Ricci and Scalar curvatures of the Bergman metric, as well as the Kobayashi–Fuks metric, at exponentially flat infinite … Abstract We prove the nontangential asymptotic limits of the Bergman canonical invariant, Ricci and Scalar curvatures of the Bergman metric, as well as the Kobayashi–Fuks metric, at exponentially flat infinite type boundary points of smooth bounded pseudoconvex domains in $$\mathbb {C}^{n + 1}, \, n \in \mathbb {N}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo>,</mml:mo> <mml:mspace/> <mml:mi>n</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> . Additionally, we establish the nontangential asymptotic limit of the Kobayashi metric at exponentially flat infinite type boundary points of smooth bounded domains in $$\mathbb {C}^{n + 1}, \, n \in \mathbb {N}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo>,</mml:mo> <mml:mspace/> <mml:mi>n</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> . We first show that these objects satisfy appropriate localizations and then utilize the method of scaling to complete the proofs.

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Toeplitz Operators with Radial Symbols on Weighted Pluriharmonic Bergman Spaces over Reinhardt Domains

2025-06-19

Sun Zhi-ling , Feng Qi , Wei–Shih Du | Axioms

In this paper, we design an operator A restricted to a weighted pluriharmonic Bergman space bμ2(Ω) over the Reinhardt domains, with an isometric isomorphism between bμ2(Ω) and the subset of … In this paper, we design an operator A restricted to a weighted pluriharmonic Bergman space bμ2(Ω) over the Reinhardt domains, with an isometric isomorphism between bμ2(Ω) and the subset of l2(Zn). Furthermore, we show that Toeplitz operators Ta with radial symbols are unitary to the multiplication operators γaI on sequence space l2 by using the operator A. The Wick function of a Toeplitz operator with a radial symbol provides some features to the operator, establishing its spectral decomposition. Finally, we specify the obtained results on the Reinhardt domains for the unit ball.

On the Symbols of Strictly m-Null Elementary Operators

2025-06-19

Isabel Marrero | Mathematics

This paper extends the previous work by the author on m-null pairs of operators in Hilbert space. If an elementary operator L has elementary symbols A and B that are … This paper extends the previous work by the author on m-null pairs of operators in Hilbert space. If an elementary operator L has elementary symbols A and B that are p-null and q-null, respectively, then L is (p+q−1)-null. Here, we prove the converse under strictness conditions, modulo some nonzero multiplicative constant—if L is strictly (p+q−1)-null, then a scalar λ≠0 exists such that λA is strictly p-null and λ−1B is strictly q-null. Our constructive argument relies essentially on algebraic and combinatorial methods. Thus, the result obtained by Gu on m-isometries is recovered without resorting to spectral analysis. For several operator classes that generalize m-isometries and are subsumed by m-null operators, the result is new.

Non-Self-Adjoint Block Convolution Operators of Scalar Type

2025-06-18

Ewelina Zalot | Complex Analysis and Operator Theory

Abstract The paper deals with the spectral theory of a class of non-self-adjoint convolution operators, which are of scalar type in the sense of Dunford. We consider the spectral decompositions … Abstract The paper deals with the spectral theory of a class of non-self-adjoint convolution operators, which are of scalar type in the sense of Dunford. We consider the spectral decompositions of such operators, focusing on the general case of operators defined on Banach spaces.

Lower Density Operators on the Plane with Borel and Non-Borel Values

2025-06-18

Gertruda Ivanova , Elżbieta Wagner-Bojakowska | Results in Mathematics

Disjoint $$\mathscr {F}$$-transitivity and topological multiple recurrence of weighted composition operators on $$H(\mathbb {D})$$

2025-06-18

Li Zhang , Cui Chen | Annals of Functional Analysis

Weighted stability estimates for maximal operators

2025-06-17

Łukasz Kamiński , Adam Osękowski | Publicacions Matemàtiques

Crossed products and $\mathrm{C}^{*}$-covers of semi-Dirichlet operator algebras

2025-06-16

Adam Humeniuk , Elias G. Katsoulis , Christopher Bronk Ramsey | Documenta Mathematica

In this paper, we show that the semi-Dirichlet \mathrm{C}^{*} -covers of a semi-Dirichlet operator algebra form a complete lattice, establishing that there is a maximal semi-Dirichlet \mathrm{C}^{*} -cover. Given an … In this paper, we show that the semi-Dirichlet \mathrm{C}^{*} -covers of a semi-Dirichlet operator algebra form a complete lattice, establishing that there is a maximal semi-Dirichlet \mathrm{C}^{*} -cover. Given an operator algebra dynamical system we prove a dilation theory that shows that the full crossed product is isomorphic to the relative full crossed product with respect to this maximal semi-Dirichlet cover. In this way, we can show that every semi-Dirichlet dynamical system has a semi-Dirichlet full crossed product.

Weighted Inequalities for Quasilinear Matrix Operators

2025-06-13

Nazerke Zhangabergenova , Ainur Temirkhanova | Journal of Mathematical Sciences

Algebraic properties of Toeplitz + Hankel operators

2025-06-13

Caixing Gu | Journal of Mathematical Analysis and Applications

Quasi-(𝑚,𝑛)-paranormal operators

2025-06-12

Baljinder Kour , Sonu Ram | Random Operators and Stochastic Equations

Abstract In this paper, we introduce the notion of quasi- <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>m</m:mi> <m:mo>,</m:mo> <m:mi>n</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> (m,n) -paranormal operators on a Hilbert space and … Abstract In this paper, we introduce the notion of quasi- <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>m</m:mi> <m:mo>,</m:mo> <m:mi>n</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> (m,n) -paranormal operators on a Hilbert space and prove basic structural properties for the same class of operators. We also characterize these operators. We prove that if 𝑇 is quasi- <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>m</m:mi> <m:mo>,</m:mo> <m:mi>n</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> (m,n) -paranormal, then the spectral mapping theorem holds, that is, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mi>f</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mi>w</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>T</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo>=</m:mo> <m:mrow> <m:mi>w</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mi>f</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>T</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> f(w(T))=w(f(T)) for every analytic function <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>f</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:mi mathvariant="script">H</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mi>σ</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>T</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> f\in\mathcal{H}(\sigma(T)) . We also show more general results for operators in the class.

On the summability of random Fourier–Jacobi series

2025-06-11

Partiswari Maharana , Sabita Sahoo | Annals of the Alexandru Ioan Cuza University - Mathematics

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At the crossroads of holomorphic dynamic and operator theory: spectral properties of composition operators on $Hol(B_N)$

2025-06-11

Lucas Oger | Canadian Mathematical Bulletin

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Dynamics of weighted composition operators on Stein manifolds

2025-06-11

Firooz Pashaie , Mohammad Reza Azimi , Sayyed Mohammad Shahidi | Annals of the Alexandru Ioan Cuza University - Mathematics

In the present paper, we investigate the hypercyclicity of weighted composition operators acting on the space of holomorphic functions on a connected finite-dimensional Stein manifold. Let ψ be a holomorphic … In the present paper, we investigate the hypercyclicity of weighted composition operators acting on the space of holomorphic functions on a connected finite-dimensional Stein manifold. Let ψ be a holomorphic self-map on a connected Stein n-manifold Ω and ω ∈ H(Ω) a holomorphic function. We study the hypercyclicity of weighted composition operator Πψ,ω : H(Ω) → H(Ω) defined by Πψ,ω (f ) := ω · (f ◦ ψ) for every f ∈ H(Ω). We prove that Πψ,ω is hypercyclic if and only if ω(p)̸ = 0 at each p ∈ Ω, ψ is univalent without fixed points in Ω, ψ(Ω) is a Runge domain and for every compact holomorphically convex set K ⊂ Ω there is an integer n such that K ∩ ψ[n](K) = ∅ and their union is holomorphically convex.

Distinguished varieties in the polydisc and dilation of commuting contractions

2025-06-07

Sourav Pal | Mathematische Zeitschrift

Invariant subspaces of Toeplitz operators with inner symbols

2025-06-02

Sumin Kim

Weighted Szegő kernels on planar domains

2025-06-01

Aakanksha Jain , Kaushal Verma | Illinois Journal of Mathematics

The Cauchy Transform on the Bergman–Dirichlet Spaces

2025-06-01

Abdelhadi Benahmadi , Abdellatif Elkachkouri , Allal Ghanmi

Certain Localization and Compactness in Bergmanand Bargmann-Fock Spaces

2025-06-01

AlaaAlhadi AlaaAlhadi , ShawgyHussein ShawgyHussein | Journal of research in applied mathematics.

The pioneers of [13] study the compactness of operators on Bergman space of the unit ball and on generally weighted Bargmann-Fock spaces in terms of their Berezin transforms and the … The pioneers of [13] study the compactness of operators on Bergman space of the unit ball and on generally weighted Bargmann-Fock spaces in terms of their Berezin transforms and the norms of the operators acting on reproducing kernels. We show how a vanishing Berezin transform combined with certain (integral) growth conditions on an operator 𝑇 are sufficient to imply that the operator is compact in the Bergman space. We also show that the reproducing kernel for compactness holds for operators satisfying similar growth conditions in (Weighted Bargmann-Fock space). Following [13] we extend the results of Xia and Zheng to the case of Bergman space when 0 < 𝜖 < ∞, and in weighted Bargmann-Fock space.The main results introduced more general new conditions that imply and improved the results of Xia and Zheng by thecase0 < 𝜖 < ∞.

A strengthening of the Harnack inequality

2025-06-01

Marek Svetlik | Indagationes Mathematicae

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A(n,m)-iso-contra-expansive operators and some applications on Bergman spaces

2025-06-01

Gherairi Khadija , Sedki Amira , Snoun Safa | Advances in Pure and Applied Mathematics

Similar operator topologies on the space of positive contractions

2024-12-16

V. Gillet

In this article, we study the similarity of the Polish operator topologies $\texttt{WOT}$, $\texttt{SOT}$, $\texttt{SOT}\mbox{$_{*}$}$ and $\texttt{SOT}\mbox{$^{*}$}$ on the set of the positive contractions on $\ell_p$ with $p > 1$. … In this article, we study the similarity of the Polish operator topologies $\texttt{WOT}$, $\texttt{SOT}$, $\texttt{SOT}\mbox{$_{*}$}$ and $\texttt{SOT}\mbox{$^{*}$}$ on the set of the positive contractions on $\ell_p$ with $p > 1$. Using the notion of norming vector for a positive operator, we prove that these topologies are similar on $\mathcal{P}_1(\ell_2)$, that is they have the same dense sets in $\mathcal{P}_1(\ell_2)$. In particular, these topologies will share the same comeager sets in $\mathcal{P}_1(\ell_2)$. We then apply these results to the study of typical properties of positive contractions on $\ell_p$-spaces in the Baire category sense. In particular, we prove that a typical positive contraction $T \in (\mathcal{P}_1(\ell_2), \texttt{SOT})$ has no eigenvalue. This stands in strong contrast to a result of Eisner and M\'atrai, stating that the point spectrum of a typical contraction $T \in (\mathcal{B}_1(\ell_2), \texttt{SOT})$ contains the whole unit disk. As a consequence of our results, we obtain that a typical positive contraction $T \in (\mathcal{P}_1(\ell_2), \texttt{WOT})$ (resp. $T \in (\mathcal{P}_1(\ell_2), \texttt{SOT}\mbox{$_{*}$})$) has no eigenvalue.

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Partially multiplicative quandles and simplicial Hurwitz spaces

2021-06-17

Andrea Bianchi

This is the first article in a series about Hurwitz spaces. We introduce the notion of partially multiplicative quandle (PMQ), which is a generalisation of the classical notions of partial … This is the first article in a series about Hurwitz spaces. We introduce the notion of partially multiplicative quandle (PMQ), which is a generalisation of the classical notions of partial abelian monoid and of quandle. We give a first, simplicial definition of Hurwitz spaces of configurations of points in the plane with monodromies in a PMQ.