OPTIMAL APPROXIMANTS AND ORTHOGONAL POLYNOMIALS IN SEVERAL VARIABLES II: FAMILIES OF POLYNOMIALS IN THE UNIT BALL

被引：5

作者：

Sargent, Meredith ^{[1
]}

Sola, Alan A. ^{[2
]}

机构：

[1] Univ Arkansas, Dept Math, Fayetteville, AR 72701 USA

[2] Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 12期

关键词：

Spaces of holomorphic functions in the unit ball; optimal approximants; orthogonal polynomials; SPACES; CYCLICITY;

D O I：

10.1090/proc/15641

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain closed expressions for weighted orthogonal polynomials and optimal approximants associated with the function f(z) = 1/root 2 (z(1) + z(2)) and a scale of Hilbert function spaces in the unit 2-ball having reproducing kernel (1 - (z,w))(-gamma), gamma > 0. Our arguments are elementary but do not rely on reduction to the one-dimensional case.

引用

页码：5321 / 5330

页数：10

共 50 条

[1] Optimal approximants and orthogonal polynomials in several variables
Sargent, Meredith
Sola, Alan A.
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2022, 74 (02): : 428 - 456
[2] Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants
Beneteau, Catherine
Khavinson, Dmitry
Liaw, Constanze
Seco, Daniel
Sola, Alan A.
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2016, 94 : 726 - 746
[3] Sobolev Orthogonal Polynomials of Several Variables on Product Domains
Duenas Ruiz, Herbert
Salazar-Morales, Omar
Pinar, Miguel
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2021, 18 (05)
[4] Sobolev Orthogonal Polynomials of Several Variables on Product Domains
Herbert Dueñas Ruiz
Omar Salazar-Morales
Miguel Piñar
Mediterranean Journal of Mathematics, 2021, 18
[5] ORTHOGONAL POLYNOMIALS AND PARTIAL DIFFERENTIAL EQUATIONS ON THE UNIT BALL
Pinar, Miguel
Xu, Yuan
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 137 (09) : 2979 - 2987
[6] Asymptotics of orthogonal polynomials inside the unit circle and Szego-Pade approximants
Rolanía, DB
Lagomasino, GL
Saff, EB
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 133 (1-2) : 171 - 181
[7] Pade approximants, continued fractions, and orthogonal polynomials
Aptekarev, A. I.
Buslaev, V. I.
Martinez-Finkelshtein, A.
Suetin, S. P.
RUSSIAN MATHEMATICAL SURVEYS, 2011, 66 (06) : 1049 - 1131
[8] Orthogonal polynomials and Pade approximants for reciprocal polynomial weights
Lubinsky, D. S.
JOURNAL OF APPROXIMATION THEORY, 2010, 162 (02) : 298 - 302
[9] On the zeros of orthogonal polynomials on the unit circle
Pilar Alfaro, Maria
Bello-Hernandez, Manuel
Maria Montaner, Jesus
JOURNAL OF APPROXIMATION THEORY, 2013, 170 : 134 - 154
[10] Multivariate orthogonal polynomials, homogeneous Padé approximants and Gaussian cubature
Brahim Benouahmane
Annie Cuyt
Numerical Algorithms, 2000, 24 : 1 - 15

← 1 2 3 4 5 →