Complex versus real orthogonal polynomials of two variables

被引：7

作者：

Xu, Yuan ^{[1
]}

机构：

[1] Univ Oregon, Dept Math, Eugene, OR 97403 USA

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2015年 / 26卷 / 02期

基金：

美国国家科学基金会;

关键词：

33C50; 33C45; disk polynomials; orthogonal polynomials of two variables; several variables; complex Hermite; complex orthogonal polynomials;

D O I：

10.1080/10652469.2014.973196

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex Hermite orthogonal polynomials and the disk polynomials are used as illustrating examples.

引用

页码：134 / 151

页数：18

共 50 条

[31] ON THE ORTHOGONAL POLYNOMIALS IN SEVERAL VARIABLES
GEKHTMAN, MI
KALYUZHNY, AA
INTEGRAL EQUATIONS AND OPERATOR THEORY, 1994, 19 (04) : 404 - 418
[32] POLYNOMIALS IN MANY VARIABLES - REAL VS COMPLEX NORMS
ARON, R
BEAUZAMY, B
ENFLO, P
JOURNAL OF APPROXIMATION THEORY, 1993, 74 (02) : 181 - 198
[33] ON REAL AND COMPLEX ZEROS OF ORTHOGONAL POLYNOMIALS IN A DISCRETE SOBOLEV SPACE
MEIJER, HG
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1993, 49 (1-3) : 179 - 191
[34] Stable and real-zero polynomials in two variables
Anatolii Grinshpan
Dmitry S. Kaliuzhnyi-Verbovetskyi
Victor Vinnikov
Hugo J. Woerdeman
Multidimensional Systems and Signal Processing, 2016, 27 : 1 - 26
[35] Stable and real-zero polynomials in two variables
Grinshpan, Anatolii
Kaliuzhnyi-Verbovetskyi, Dmitry S.
Vinnikov, Victor
Woerdeman, Hugo J.
MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING, 2016, 27 (01) : 1 - 26
[36] Łojasiewicz inequality at infinity for polynomials in two real variables
Ha Huy Vui
Nguyen Hong Duc
Mathematische Zeitschrift, 2010, 266 : 243 - 264
[37] On the development of a function of two real variables into series of polynomials
Thijsen, WP
PROCEEDINGS OF THE KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM, 1927, 30 (1/5): : 69 - 80
[38] Lojasiewicz inequality at infinity for polynomials in two real variables
Ha Huy Vui
Nguyen Hong Duc
MATHEMATISCHE ZEITSCHRIFT, 2010, 266 (02) : 243 - 264
[39] Topological types of polynomials of two complex variables at infinity
Fourrier, L
ANNALES DE L INSTITUT FOURIER, 1996, 46 (03) : 645 - &
[40] UPPER BOUNDS OF TOPOLOGY OF COMPLEX POLYNOMIALS IN TWO VARIABLES
Glutsyuk, A. A.
MOSCOW MATHEMATICAL JOURNAL, 2005, 5 (04) : 781 - 828

← 1 2 3 4 5 →