Ramanujan's Master Theorem for the Hypergeometric Fourier Transform Associated with Root Systems

被引:16
作者
Olafsson, G. [1 ]
Pasquale, A. [2 ]
机构
[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
[2] Univ Lorraine, UMR CNRS 7502, Inst Elie Cartan Lorraine, F-57045 Metz, France
基金
美国国家科学基金会;
关键词
Ramanujan's Master theorem; Hypergeometric functions; Jacobi polynomials; Spherical functions; Root systems; Cherednik operators; Hypergeometric Fourier transform; COMPACT SYMMETRICAL SPACE; PALEY-WIENER THEOREM; COMPLEXIFICATION;
D O I
10.1007/s00041-013-9290-5
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Ramanujan's Master theorem states that, under suitable conditions, the Mellin transform of an alternating power series provides an interpolation formula for the coefficients of this series. Ramanujan applied this theorem to compute several definite integrals and power series, which explains why it is referred to as the "Master Theorem". In this paper we prove an analogue of Ramanujan's Master theorem for the hypergeometric Fourier transform associated with root systems. This theorem generalizes to arbitrary positive multiplicity functions the results previously proven by the same authors for the spherical Fourier transform on semisimple Riemannian symmetric spaces.
引用
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页码:1150 / 1183
页数:34
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