The spectrum of the right inverse of the Dunkl operator

被引：2

作者：

Abreu, Luis Daniel ^{[1
,2
]}

Ciaurri, Oscar ^{[3
,4
]}

Luis Varona, Juan ^{[3
,4
]}

机构：

[1] Univ Coimbra, CMUC, P-3001454 Coimbra, Portugal

[2] Univ Coimbra, Dept Matemat, Fac Ciencias & Tecnol FCTUC, P-3001454 Coimbra, Portugal

[3] Univ La Rioja, CIME, Logrono 26004, Spain

[4] Univ La Rioja, Dept Matemat & Computac, Logrono 26004, Spain

来源：

REVISTA MATEMATICA COMPLUTENSE | 2013年 / 26卷 / 02期

基金：

奥地利科学基金会;

关键词：

Plane wave expansion; Dunkl operator; Dunkl kernel; Spectrum; Diagonalization of operators; Special functions; DIAGONALIZATION; TRANSFORM;

D O I：

10.1007/s13163-012-0110-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

From the Dunkl analogue of Gegenbauer's expansion of the plane wave, we derive an explicit closed formula for the spectrum of a right inverse of the Dunkl operator. This is done by stating the problem in such a way it is possible to use the technique due to Ismail and Zhang.

引用

页码：471 / 483

页数：13

共 18 条

[1]

Abramowitz M., 1964, HDB MATH FUNCTIONS F

[2] Bilinear biorthogonal expansions and the Dunkl kernel on the real line [J].