Uniform Approximation of Extremal Functions in Weighted Bergman Spaces

被引：0

作者：

Ferguson, Timothy ^{[1
]}

机构：

[1] Univ Alabama, Dept Math, Tuscaloosa, AL 35487 USA

来源：

COMPUTATIONAL METHODS AND FUNCTION THEORY | 2018年 / 18卷 / 03期

关键词：

Bergman space; Extremal problem; Polyomial approximation; Holder continuity;

D O I：

10.1007/s40315-017-0230-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss approximation of extremal functions by polynomials in the weighted Bergman spaces where . We obtain bounds on how close the approximation is to the true extremal function in the and uniform norms. We also prove several results on the relation between the Bergman modulus of continuity of a function and how quickly its best polynomial approximants converge to it.

引用

页码：439 / 453

页数：15

共 50 条

[1] Uniform Approximation of Extremal Functions in Weighted Bergman Spaces
Timothy Ferguson
Computational Methods and Function Theory, 2018, 18 : 439 - 453
[2] Extremal functions in weighted Bergman spaces
Nowak, M. T.
Rososzczuk, R.
Woloszkiewicz-Cyll, M.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2017, 62 (01) : 98 - 109
[3] Zeros of extremal functions in weighted Bergman spaces
Weir, RJ
PACIFIC JOURNAL OF MATHEMATICS, 2003, 208 (01) : 187 - 199
[4] REGULARITY OF EXTREMAL FUNCTIONS IN WEIGHTED BERGMAN AND FOCK TYPE SPACES
Ferguson, Timothy
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2019, 49 (01) : 47 - 71
[5] Some remarks on extremal problems in weighted Bergman spaces of analytic functions
Shamoyan, Romi F.
Arsenovic, Milos
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2012, 27 (04): : 753 - 762
[6] On the best approximation of some classes of analytic functions in weighted Bergman spaces
M. Sh. Shabozov
O. Sh. Shabozov
Doklady Mathematics, 2007, 75 : 97 - 100
[7] On the best approximation of some classes of analytic functions in weighted Bergman spaces
Shabozov, M. Sh.
Shabozov, O. Sh.
DOKLADY MATHEMATICS, 2007, 75 (01) : 97 - 100
[8] Multiple interpolation and extremal functions in the Bergman spaces
Mark Krosky
Alexander P. Schuster
Journal d’Analyse Mathématique, 2001, 85 : 141 - 156
[9] Multiple interpolation and extremal functions in the Bergman spaces
Krosky, M
Schuster, AP
JOURNAL D ANALYSE MATHEMATIQUE, 2001, 85 (1): : 141 - 156
[10] Generalized interpolation in Bergman spaces and extremal functions
Hartmann, A
MATHEMATISCHE NACHRICHTEN, 2001, 224 : 123 - 144

← 1 2 3 4 5 →