On uniform approximation by polyanalytic polynomials and the Dirichlet problem for bianalytic functions

被引：31

作者：

Carmona, JJ ^{[1
]}

Paramonov, PV

Fedorovskii, KY

机构：

[1] Univ Autonoma Barcelona, E-08193 Barcelona, Spain

[2] Moscow MV Lomonosov State Univ, Moscow, Russia

[3] State Univ Management, Moscow, Russia

来源：

SBORNIK MATHEMATICS | 2002年 / 193卷 / 9-10期

关键词：

D O I：

10.1070/SM2002v193n10ABEH000690

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

New necessary and, sufficient conditions for the uniform approximability of functions by polyanalytic polynomials and polyanalytic rational functions on compact subsets of the plane are established. Connections between these approximation problems and the Dirichlet problem for bianalytic functions are also analysed.

引用

页码：1469 / 1492

页数：24

共 50 条

[1] The Dirichlet problem for polyanalytic functions
Mazalov, M. Ya.
SBORNIK MATHEMATICS, 2009, 200 (9-10) : 1473 - 1493
[2] Uniform and Cm-Approximation by Polyanalytic Polynomials
Fedorovskiy, Konstantin Yu
COMPLEX ANALYSIS AND POTENTIAL THEORY, 2012, 55 : 323 - 329
[3] New conditions for uniform approximation by polyanalytic polynomials
J. J. Carmona
K. Yu. Fedorovskiy
Proceedings of the Steklov Institute of Mathematics, 2012, 279 : 215 - 229
[4] New conditions for uniform approximation by polyanalytic polynomials
Carmona, J. J.
Fedorovskiy, K. Yu.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2012, 279 (01) : 215 - 229
[5] THE SOLUTION TO THE DIRICHLET PROBLEM FOR POLYANALYTIC FUNCTIONS IN DOMAINS WITH ALGEBRAIC BOUNDARIES
RASULOV, KM
DIFFERENTIAL EQUATIONS, 1995, 31 (01) : 95 - 101
[6] Uniform approximation by harmonic polynomials for solving the Dirichlet problem of Laplace's equation on a disk
Lee, Haesung
LITHUANIAN MATHEMATICAL JOURNAL, 2025,
[7] UNIFORM APPROXIMATION BY POLYNOMIALS IN 2 FUNCTIONS
OFARRELL, AG
PRESKENIS, KJ
MATHEMATISCHE ANNALEN, 1989, 284 (04) : 529 - 535
[8] METHODS OF APPROXIMATION OF FUNCTIONS IN INVARIANT SUBSPACES BY DIRICHLET POLYNOMIALS
KRASICHKOVTERNOVSKII, IF
SIBERIAN MATHEMATICAL JOURNAL, 1975, 16 (05) : 779 - 787
[9] UNIFORM ESTIMATES OF THE COCONVEX APPROXIMATION OF FUNCTIONS BY POLYNOMIALS
KOPOTUN, KA
MATHEMATICAL NOTES, 1992, 51 (3-4) : 245 - 254
[10] UNIFORM APPROXIMATION BY SPLINES OF POLYNOMIALS AND OF ENTIRE FUNCTIONS
RUBEL, LA
VENKATES.S
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (07): : A635 - A635

← 1 2 3 4 5 →