Krein's entire functions and the Bernstein approximation problem

Alexander Borichev, Mikhail Sodin

Type: Article

Publication Date: 2001-01-01

Citations: 33

DOI: https://doi.org/10.1215/ijm/1258138261

Abstract

We extend two theorems of Krein concerning entire functions of Cartwright class, and give applications for the Bernstein weighted approximation problem. The Krein class and functions of bounded typeWe start with two classical theorems of Krein concerning entire functions.An entire function f belongs to the Cartwright class if f has at most exponential type, that is, ifand the logarithmic integral converges:

Locations

Illinois Journal of Mathematics - View - PDF

Similar Works

Action	Title	Year	Authors
+	Krein's entire functions and the Bernstein approximation problem	2000	Alexander Borichev Mikhail Sodin
+	Two Elementary Properties of Entire Functions and Their Applications	2015	Bao Qin Li
+	On Bernstein's inequality for entire functions of exponential type	2009	Q. I. Rahman Q. M. Tariq
+	De Branges' theorem on approximation problems of Bernstein type	2012	Anton Baranov Harald Woracek
+	De Branges' theorem on approximation problems of Bernstein type	2012	Anton Baranov Harald Woracek
+	On Bernstein’s Inequality for Entire Functions of Exponential Type	2006	Q. I. Rahman Q. M. Tariq
+ PDF Chat	De Branges’ theorem on approximation problems of Bernstein type	2013	Anton Baranov Harald Woracek
+	On a refinement of the bernstein inequality for entire functions of exponential type	1996	Q. I. Rahman Gerhard Schmeißer
+ PDF Chat	Inequalities and representation formulas for functions of exponential type	1995	Clément Frappier Patrick Olivier
+	S. N. Bernstein’s inequality for entire functions of exponential type and its generalizations	1996	B. Yu. Levin
+	A Borel-Carathéodory inequality and approximation of entire functions by polynomials with restricted zeros	1971	J.M Elkins
+	Entire Functions in Generalized Bernstein Spaces and Their Growth Behavior	2015	Brigitte Forster Gunter Semmler
+	Bernstein Functions	2012	René L. Schilling Renming Song Zoran Vondraček
+	Introduction to the Theory of Entire Functions	1973	A. S. B. Holland
+	The Bernstein-Widder theorem on completely monotonic functions	1944	Harry Pollard
+ PDF Chat	Entire functions that deviate least from zero in the uniform and the integral metrics with a weight	2015	A. V. Gladkaya O. L. Vinogradov
+	Bernstein Functions	2009	René L. Schilling Renming Song Zoran Vondraček
+	The Pólya Representation Theorem	1996	Lee A. Rubel J. Colliander
+	Functions of exponential type in a half-plane	2011	Mohammed A. Qazi Q. I. Rahman
+ PDF Chat	Approximation by entire functions.	1955	Wilfred Kaplan

Works That Cite This (32)

Action	Title	Year	Authors
+ PDF Chat	Martin Functions of Fuchsian Groups and Character Automorphic Subspaces of the Hardy Space in the Upper Half Plane	2020	Alexander Kheifets Peter Yuditskii
+	The Riemann Hypothesis, Dilations, and<i>H</i><sup>2</sup>in the Hilbert Multi-disk	2019	Nikolaï Nikolski
+ PDF Chat	Reflectionless canonical systems, II. Almost periodicity and character-automorphic Fourier transforms	2024	Roman Bessonov Milivoje Lukić Peter Yuditskii
+ PDF Chat	Asymptotic Properties of Entire Functions with Given Laws of Distribution of Zeros	2021	V. B. Sherstyukov
+	On the Direct Cauchy Theorem in Widom Domains: Positive and Negative Examples Peter Yuditskii	2012	Peter Yuditskii
+ PDF Chat	On the completeness of the system $$\{ {t^{{\lambda _n}}}{\log ^{{m_n}}}t\} $$ in C 0(E)	2012	Xiangdong Yang
+	Key Notions of Linear Operators	2019	Nikolaï Nikolski
+	Key Notions of Banach spaces	2019	Nikolaï Nikolski
+	Key Notions of Hilbert Spaces	2019	Nikolaï Nikolski
+	The Origins of the Subject	2019	Nikolaï Nikolski

Works Cited by This (14)

Action	Title	Year	Authors
+	Hilbert spaces of entire functions	1968	Louis de Branges
+	The logarithmic integral	1986	Paul Koosis
+ PDF Chat	On the distribution of values of meromorphic functions	1968	Fred Gross
+	Entire functions and trigonometric polynomials	1953	A. C. Schaeffer
+ PDF Chat	On fourier transforms of measures with compact support	1962	Arne Beurling Paul Malliavin
+ PDF Chat	The Bernstein problem	1959	Louis de Branges
+ PDF Chat	Positive harmonic functions vanishing on the boundary of certain domains in Rn	1980	Michael Benedicks
+	Lectures on entire functions	1996	B. Yu. Levin
+	Sur les moyennes des fonctions harmoniques et analytiques et la classification des surfaces de Riemann	1951	Michel Parreau
+	LECTURES ON ENTIRE FUNCTIONS (Translations of Mathematical Monographs 150)	1998	W. K. Hayman