A Whittaker-Shannon-Kotel'nikov sampling theorem related to the Dunkl transform

被引：23

作者：

Ciaurri, Oscar ^{[1
]}

Varona, Juan L. ^{[1
]}

机构：

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

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2007年 / 135卷 / 09期

关键词：

WSK sampling theorem; reproducing kernel; Dunkl transform; orthonormal system; Bessel functions;

D O I：

10.1090/S0002-9939-07-08831-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A Whittaker-Shannon-Kotel'nikov sampling theorem related to the Dunkl transformon the real line is proved. To this end we state, in terms of Bessel functions, an orthonormal system which is complete in L-2((-1, 1), vertical bar x vertical bar (2 alpha+1) dx). This orthonormal system is a generalization of the classical exponential system de. ning Fourier series.

引用

页码：2939 / 2947

页数：9

共 18 条

[1] A q-sampling theorem related to the q-Hankel transform [J].

Abreu, LD .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (04) :1197-1203

[2]

Andersen NB, 2005, INT MATH RES NOTICES, V2005, P1817

[3]

BETANCOR J, IN PRESS J FUNCT ANA

[4] Mean and almost everywhere convergence of Fourier-Neumann series [J].

Ciaurri, O ;

Guadalupe, JJ ;

Pérez, M ;

Varona, JL .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 236 (01) :125-147

[5] THE DUNKL TRANSFORM [J].

DEJEU, MFE .

INVENTIONES MATHEMATICAE, 1993, 113 (01) :147-162

[6] DIFFERENTIAL-DIFFERENCE OPERATORS ASSOCIATED TO REFLECTION GROUPS [J].

DUNKL, CF .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 311 (01) :167-183

[7] INTEGRAL-KERNELS WITH REFLECTION GROUP INVARIANCE [J].

DUNKL, CF .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1991, 43 (06) :1213-1227

[8] Orthogonal sampling formulas: A unified approach [J].

Garcia, AG .

SIAM REVIEW, 2000, 42 (03) :499-512

[9]

HIGGINS JR, 1972, J LOND MATH SOC, V5, P707

[10] A q-analogue of the Whittaker-Shannon-Kotelnikov sampling theorem [J].

Ismail, ME ;

Zayed, AI .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (12) :3711-3719

← 1 2 →