Characterization of the support for the hypergeometric Fourier transform of the W-invariant functions and distributions on Rd and Roe's theorem

被引：14

作者：

Mejjaoli, Hatem ^{[1
]}

Trimeche, Khalifa ^{[2
]}

机构：

[1] Taibah Univ, Coll Sci, Dept Math, Al Madinah Al Munawarah, Saudi Arabia

[2] Univ Tunis El Manar, Fac Sci, Dept Math, Tunis 1060, Tunisia

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2014年

关键词：

Cherednik operators; Heckman-Opdam Laplacian; hypergeometric Fourier transform; real Paley-Wiener theorems; Roe's theorem; EIGENFUNCTIONS;

D O I：

10.1186/1029-242X-2014-99

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish real Paley-Wiener theorems for the hypergeometric Fourier transform on R-d. More precisely, we characterize the functions of the generalized Schwartz space S-2(R-d)(W) and of L-Ak(p) (R-d)(W), 1 <= p <= 2, whose hypergeometric Fourier transform has bounded, unbounded, convex, and nonconvex support. Finally we study the spectral problem on the generalized tempered distributions S'(2) (R-d)(W).

引用

页数：26

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