On a general q-Fourier transformation with nonsymmetric kernels

被引：38

作者：

Askey, RA

Rahman, M

Suslov, SK

机构：

[1] UNIV WISCONSIN,DEPT MATH,MADISON,WI 53706

[2] CARLETON UNIV,DEPT MATH & STAT,OTTAWA,ON K1S 5B6,CANADA

[3] IV KURCHATOV ATOM ENERGY INST,RUSSIAN RES CTR,MOSCOW 123182,RUSSIA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1996年 / 68卷 / 1-2期

基金：

美国国家科学基金会;

关键词：

q-Fourier transform; integral transforms; q-orthogonal polynomials; Hermite polynomials; Poisson kernels; Fourier transform; basic hypergeometric series; Askey-Wilson polynomials; Al-Salam-Chihara polynomials;

D O I：

10.1016/0377-0427(95)00259-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Wiener used the Poisson kernel for the Hermite polynomials to deal with the classical Fourier transform. Askey, Atakishiyev and Suslov used this approach to obtain a q-Fourier transform by using the continuous q-Hermite polynomials. Rahman and Suslov extended this result by taking the Askey-Wilson polynomials, considered to be the most general continuous classical orthogonal polynomials. The theory of q-Fourier transformation is further extended here by considering a nonsymmetric version of the Poisson kernel with Askey-Wilson polynomials. This approach enables us to obtain some new results, for example, the complex and real orthogonalities of these kernels.

引用

页码：25 / 55

页数：31

共 21 条

[1] THE Q-HARMONIC OSCILLATOR AND THE AL-SALAM AND CARLITZ POLYNOMIALS [J].