A. Cachafeiro

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All published works

Action	Title	Year	Authors
+ PDF Chat	A Type of Interpolation between Those of Lagrange and Hermite That Uses Nodal Systems Satisfying Some Separation Properties	2024	E. Berriochoa A. Cachafeiro Héctor García Rábade J. García-Amor
+ PDF Chat	A Note on Lagrange Interpolation of \|x\| on the Chebyshev and Chebyshev–Lobatto Nodal Systems: The Even Cases	2022	E. Berriochoa A. Cachafeiro Héctor García Rábade J. García-Amor
+	The Gibbs–Wilbraham phenomenon in the approximation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e870" altimg="si5.svg"><mml:mrow><mml:mo>\|</mml:mo><mml:mi>x</mml:mi><mml:mo>\|</mml:mo></mml:mrow></mml:math> by using Lagrange interpolation on the Chebyshev–Lobatto nodal systems	2022	E. Berriochoa A. Cachafeiro J. García-Amor Héctor García Rábade
+ PDF Chat	Classical Lagrange Interpolation Based on General Nodal Systems at Perturbed Roots of Unity	2020	E. Berriochoa A. Cachafeiro Alberto Castejón J. García-Amor
+	Gibbs–Wilbraham phenomenon on Lagrange interpolation based on analytic weights on the unit circle	2019	E. Berriochoa A. Cachafeiro J.M. García Amor
+	Szegő transformation and zeros of analytic perturbations of Chebyshev weights	2018	E. Berriochoa A. Cachafeiro Francisco Marcellán
+ PDF Chat	Gibbs–Wilbraham oscillation related to an Hermite interpolation problem on the unit circle	2018	E. Berriochoa A. Cachafeiro J.M. García Amor
+	About Nodal systems for Lagrange interpolation on the circle	2017	E. Berriochoa A. Cachafeiro J.M. García Amor
+	An interpolation problem on the circle between Lagrange and Hermite problems	2016	E. Berriochoa A. Cachafeiro J.M. García Amor
+ PDF Chat	A note on the rate of convergence for Chebyshev-Lobatto and Radau systems	2016	E. Berriochoa A. Cachafeiro Jaime Díaz Eduardo Martı́nez
+	On the asymptotic constant for the rate of Hermite–Fejér convergence on Chebyshev nodes	2015	E. Berriochoa A. Cachafeiro
+	Gibbs phenomenon in the Hermite interpolation on the circle	2015	E. Berriochoa A. Cachafeiro J. Díaz
+	Convergence of Hermite interpolants on the circle using two derivatives	2014	E. Berriochoa A. Cachafeiro J. Díaz
+	Algorithms and convergence for Hermite interpolation based on extended Chebyshev nodal systems	2014	E. Berriochoa A. Cachafeiro J. Díaz Juan Carlos Sánchez Illán
+ PDF Chat	Hermite Interpolation on the Unit Circle Considering up to the Second Derivative	2014	E. Berriochoa A. Cachafeiro Jaime Díaz
+ PDF Chat	Modified Gauss rules for approximate calculation of some strongly singular integrals	2013	E. Berriochoa A. Cachafeiro Juan Carlos Sánchez Illán J.M. Rebollido
+	Asymptotic constants for the error of Hermite-Fejér interpolation on the unit circle	2013	A. Cachafeiro E. Berriochoa J. Díaz Eduardo Martı́nez
+ PDF Chat	Rate of Convergence of Hermite-Fejér Interpolation on the Unit Circle	2013	E. Berriochoa A. Cachafeiro J. Díaz E. Martínez-Brey
+ PDF Chat	About Nodal Systems for Lagrange Interpolation on the Circle	2012	E. Berriochoa A. Cachafeiro J.M. García Amor
+	About measures and nodal systems for which the Hermite interpolants uniformly converge to continuous functions on the circle and interval	2011	E. Berriochoa A. Cachafeiro Eduardo Martı́nez
+	An Extension of Fejér’s Condition for Hermite Interpolation	2011	E. Berriochoa A. Cachafeiro J. García-Amor
+	Some improvements to the Hermite–Fejér interpolation on the circle and bounded interval	2011	E. Berriochoa A. Cachafeiro E. Martínez Brey
+	Complex measures having quadrature formulae with optimal exactness	2009	E. Berriochoa A. Cachafeiro J. García-Amor
+	Quadrature rules for polynomial modifications of Bernstein measures exact for analytic functions	2009	E. Berriochoa A. Cachafeiro J. García-Amor
+	Characterizing the measures on the unit circle with exact quadrature formulas in the space of polynomials	2009	E. Berriochoa A. Cachafeiro J. García Amor
+	Algorithms for solving Hermite interpolation problems using the Fast Fourier Transform	2009	E. Berriochoa A. Cachafeiro
+	A bi-orthogonal system of trigonometric functions	2009	E. Berriochoa A. Cachafeiro J. García-Amor
+	Characterizing curves satisfying the Gauss–Christoffel theorem	2009	E. Berriochoa A. Cachafeiro
+	Characterizing orthogonality measures on the bounded interval<sup>1</sup>	2008	A. Cachafeiro C. Pérez
+	About a system of anti-periodic trigonometric functions	2008	E. Berriochoa A. Cachafeiro J. García-Amor
+	NEW QUADRATURE RULES FOR BERNSTEIN MEASURES ON THE INTERVAL	2008	A. Cachafeiro Eloy Garc
+ PDF Chat	A new numerical quadrature formula on the unit circle	2007	E. Berriochoa A. Cachafeiro Francisco Marcellán
+	A SYSTEM OF BIORTHOGONAL TRIGONOMETRIC POLYNOMIALS	2007	E. Berriochoa A. Cachafeiro J. García-Amor
+	Nodal systems with maximal domain of exactness for Gaussian quadrature formulas	2007	E. Berriochoa A. Cachafeiro
+ PDF Chat	Orthogonal polynomials with respect to the sum of an arbitrary measure and a Bernstein–Szegö measure	2006	A. Cachafeiro Francisco Marcellán C. Pérez
+	Quasi-orthogonality properties and orthogonality with respect to the Chebyshev perturbation of a Bernstein measure	2006	E. Berriochoa A. Cachafeiro J. García-Amor
+	A scalar Riemann boundary value problem approach to orthogonal polynomials on the circle	2006	Alexander Ivanovich Aptekarev A. Cachafeiro Francisco Marcellán
+	Asymptotics on the support for sobolev orthogonal polynomials on a bounded interval	2005	E. Berriochoa A. Cachafeiro J. García-Amor
+	Connections between Interval and Unit Circle for Sobolev Orthogonal Polynomials. Strong Asymptotics on the Real Line	2005	E. Berriochoa A. Cachafeiro J. Garc�a-Amor
+ PDF Chat	A characterization of the four Chebyshev orthogonal families	2005	E. Berriochoa A. Cachafeiro J. García-Amor
+	Connection between orthogonal polynomials on the unit circle and bounded interval	2004	E. Berriochoa A. Cachafeiro J. García-Amor
+	Asymptotic properties of Chebyshev–Sobolev orthogonal polynomials	2004	E. Berriochoa A. Cachafeiro J. García-Amor
+	Second degree functionals on the unit circle	2004	A. Cachafeiro C. Pérez
+ PDF Chat	On asymptotic properties of Freud–Sobolev orthogonal polynomials	2003	A. Cachafeiro Francisco Marcellán Juan J. Moreno–Balcázar
+	Extension inside the disk of asymptotics for Sobolev orthogonal polynomials	2003	E. Berriochoa A. Cachafeiro
+	A necessary condition for the extension of Szegő's asymptotics inside the disk in the Sobolev case	2003	E. Berriochoa A. Cachafeiro
+	Lebesgue perturbation of a quasi-definite Hermitian functional. The positive definite case	2003	A. Cachafeiro Francisco Marcellán C. Pérez
+	On the Strong Asymptotics for Sobolev Orthogonal Polynomials on the Circle	2003	E. Berriochoa A. Cachafeiro
+	Second kind functionals for the Laguerre-Hahn affine class on the unit circle	2003	A. Cachafeiro Francisco Marcellán C. Pérez
+	Differential properties for a class of Sobolev orthogonal polynomials	2002	E. Berriochoa A. Cachafeiro
+	Strong asymptotics inside the unit disk for Sobolev orthogonal polynomials	2002	E. Berriochoa A. Cachafeiro
+	Asymptotic behavior inside the disk for Lebesgue Sobolev orthogonal polynomials	2002	E. Berriochoa A. Cachafeiro
+ PDF Chat	Differential properties for Sobolev orthogonality on the unit circle	2001	E. Berriochoa A. Cachafeiro Francisco Marcellán
+	Polynomials with minimal norm and new results in Szegő's theory	2000	E. Berriochoa A. Cachafeiro
+	Bernstein-szegö-lebesgue sobolev orthogonal polynomials on the unit circle	2000	E. Berriochoa A. Cachafeiro
+	Strong Asymptotics for the Continuous Sobolev Orthogonal Polynomials on the Unit Circle	1999	Alexander Ivanovich Aptekarev E. Berriochoa A. Cachafeiro
+	A family of Sobolev orthogonal polynomials on the unit circle	1999	E. Berriochoa A. Cachafeiro
+ PDF Chat	A study of the generalized Christoffel functions with applications	1999	E. Berriochoa A. Cachafeiro Francisco Marcellán
+	Lebesgue Sobolev orthogonality on the unit circle	1998	E. Berriochoa A. Cachafeiro
+ PDF Chat	Convex linear combinations of sequences of monic orthogonal polynomials	1998	A. Cachafeiro Francisco Marcellán
+	About semiclassical polynomials on the unit circle corresponding to the class (2,2)	1997	A. Cachafeiro Carmen Becerra Suárez
+	Orthogonal polynomials related to the unit circle and differential-difference equations	1997	A. Cachafeiro Carmen Becerra Suárez
+	Kernels on the unit circle. Orthogonality	1996	A. Cachafeiro Carmen Becerra Suárez
+	A generalization of the associated functional to the Lebesgue measure	1995	Ma Concepción Agras Suárez A. Cachafeiro
+	Orthogonal Polynomials of Sobolev Type on the Unit Circle	1994	A. Cachafeiro Francisco Marcellán
+	Inverse Problems: Rational Modifications	1994	A. Cachafeiro Carmen Becerra Suárez
+ PDF Chat	Modifications of Toeplitz Matrices: Jump Functions	1993	A. Cachafeiro Francisco Marcellán
+	Perturbations in Toeplitz matrices. II. Asymptotic properties	1991	A. Cachafeiro Francisco Marcellán
+	The characterization of the quasi-typical extension of an inner product	1990	A. Cachafeiro Francisco Marcellán

Common Coauthors

Coauthor	Papers Together
E. Berriochoa	51
J. García-Amor	15
Francisco Marcellán	14
J. Díaz	5
J.M. García Amor	5
C. Pérez	5
Carmen Becerra Suárez	4
Eduardo Martı́nez	3
Héctor García Rábade	3
Jaime Díaz	2
Juan Carlos Sánchez Illán	2
Alexander Ivanovich Aptekarev	2
E. Martínez Brey	1
E. Martínez-Brey	1
J. García Amor	1
Eloy Garc	1
Juan J. Moreno–Balcázar	1
Alberto Castejón	1
Ma Concepción Agras Suárez	1
J.M. Rebollido	1
J. GarcÍa-Amor	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Orthogonal Polynomials	1971		28
+	On orthogonal polynomials	1975	P. Túrán	15
+	Orthogonal polynomials	2022	T. W. Körner Terence Tao	13
+	A note on hermite-fejér interpolation for the unit circle	2001	Leyla Daruis Pablo González-Vera	12
+ PDF Chat	On Orthogonal Polynomials	1961	Burton Wendroff	12
+	Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle	1989	William B. Jones Olav Njåstad W. J. Thron	11
+	The Chebyshev polynomials	1974	T. J. Rivlin	10
+	Orthogonal Polynomials on the Unit Circle	2005	Barry Simon	10
+	Polynomials orthogonal on a circle and their applications	1954	Я. Л. Геронимус	10
+	Topics in Polynomials	1994	Gradimir V. Milovanović D. S. Mitrinović Th. M. Rassias	8
+	Approximation Theory and Approximation Practice	2013	Lloyd N. Trefethen	8
+	Some improvements to the Hermite–Fejér interpolation on the circle and bounded interval	2011	E. Berriochoa A. Cachafeiro E. Martínez Brey	7
+	Interpolation and Approximation by Rational Functions in the Complex Domain	1935	J. L. Walsh	7
+	Bernstein—Szegő's Theorem for Sobolev Orthogonal Polynomials	2000	Andrei Martı́nez-Finkelshtein	6
+	Toeplitz Forms and Their Applications.	1958	Leonard J. Savage Ulf Grenander Gábor Szegő	6
+	Connection between orthogonal polynomials on the unit circle and bounded interval	2004	E. Berriochoa A. Cachafeiro J. García-Amor	6
+	Algorithms for solving Hermite interpolation problems using the Fast Fourier Transform	2009	E. Berriochoa A. Cachafeiro	6
+	<i>Toeplitz Forms and Their Applications</i>	1958	Ulf Grenander Gábor Szegő Mark Kac	6
+	Orthogonal Polynomials	1972	Albert L. Rabenstein	6
+	Gibbs phenomenon in the Hermite interpolation on the circle	2015	E. Berriochoa A. Cachafeiro J. Díaz	5
+	Chebyshev Polynomials	2002	J. C. Mason D. C. Handscomb	5
+ PDF Chat	Gaussian quadrature formulae on the unit circle	2002	Leyla Daruis Pablo González-Vera Francisco Marcellán	5
+	The extended Hermite--Fejér interpolation formula with appplication to the theory of generalized almost-step parabolas	2022	Paul C. Szasz	5
+	Strong Asymptotics for the Continuous Sobolev Orthogonal Polynomials on the Unit Circle	1999	Alexander Ivanovich Aptekarev E. Berriochoa A. Cachafeiro	5
+	None	2002	Leonid Golinski	5
+	Real and Complex Analysis.	1987	G. A. Garreau Walter Rudin	5
+ PDF Chat	Rate of Convergence of Hermite-Fejér Interpolation on the Unit Circle	2013	E. Berriochoa A. Cachafeiro J. Díaz E. Martínez-Brey	5
+	On the Strong Asymptotics for Sobolev Orthogonal Polynomials on the Circle	2003	E. Berriochoa A. Cachafeiro	4
+	A special class of polynomials orthogonal on the unit circle including the associated polynomials	1996	Franz Peherstorfer	4
+	INTERPOLATION AND APPROXIMATION	1983	James S. Vandergraft	4
+	Special linear combinations of orthogonal polynomials	2004	Zinoviy Grinshpun	4
+	Second kind functionals for the Laguerre-Hahn affine class on the unit circle	2003	A. Cachafeiro Francisco Marcellán C. Pérez	4
+	A Limit Function for Equidistant Fourier Interpolation	1995	Gilbert Helmberg	4
+	Essentials of numerical analysis, with pocket calculator demonstrations	1982	Peter Henrici	4
+	On some open problems of approximation theory	1980	P. Túrán	4
+	Lebesgue Sobolev orthogonality on the unit circle	1998	E. Berriochoa A. Cachafeiro	4
+	Comportamiento asintótico de polinomios ortogonales tipo Sobolev	2011	Foulquié Moreno Ana Pilar	4
+	An Extension of Fejér’s Condition for Hermite Interpolation	2011	E. Berriochoa A. Cachafeiro J. García-Amor	4
+	About measures and nodal systems for which the Hermite interpolants uniformly converge to continuous functions on the circle and interval	2011	E. Berriochoa A. Cachafeiro Eduardo Martı́nez	4
+	On general Hermite trigonometric interpolation	1972	Rainer Kreß	3
+ PDF Chat	Orthogonal Polynomials and their Applications	1988		3
+	The Chebyshev Polynomials	2002		3
+	Gibbs–Wilbraham phenomenon on Lagrange interpolation based on analytic weights on the unit circle	2019	E. Berriochoa A. Cachafeiro J.M. García Amor	3
+ PDF Chat	Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product	1995	G. López Lagomasino Francisco Marcellán Walter Van Assche	3
+ PDF Chat	A new numerical quadrature formula on the unit circle	2007	E. Berriochoa A. Cachafeiro Francisco Marcellán	3
+	An Introduction to Orthogonal Polynomials	2020	M. Foupouagnigni	3
+	A family of Sobolev orthogonal polynomials on the unit circle	1999	E. Berriochoa A. Cachafeiro	3
+	The connection between systems of polynomials orthogonal with respect to different distribution functions	1969	Vasilii B. Uvarov	3
+	Asymptotic properties of Sobolev orthogonal polynomials	1998	Andrei Martı́nez-Finkelshtein	3
+	Fine Structure of the Zeros of Orthogonal Polynomials, I. A Tale of Two Pictures	2004	Barry Simon	3