Ramanujan's master theorem and duality of symmetric spaces
type: Item
instance of: scholarly article
title: Ramanujan's master theorem and duality of symmetric spaces
zbMATH Open document ID: 0880.43012
author: Wolfgang Bertram
published in: Journal of Functional Analysis
publication date: 1998-02-01T00:00:00Z
review text: The author studies Ramanujan's ``Master Theorem'', which consists of the formula \[ \int^\infty_0 x^{-s-1} \sum^\infty_{k=0} \bigl[(-1)^k a(k)x^k \bigr] dx= -{\pi \over \sin (\pi s)} a(s). \] He interprets this relation as one between Fourier transforms of an analytic function \(f\) with respect to the real forms \(U(1)\) (compact) and \(\mathbb{R}^+\) (noncompact) of the multiplicative group of non-zero complex numbers. The rank one case is treated in detail in the present paper.
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 1054125
zbMATH Keywords: symmetric space
zbMATH Keywords: Ramanujan's master theorem
zbMATH Keywords: Fourier transforms
zbMATH Keywords: analytic function
reviewed by: Steven G. Krantz
MaRDI profile type: Publication
full work available at URL: jfan.1996.3051
OpenAlex ID: W1973359419
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DOI: 10.1006/JFAN.1996.3051
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description: scientific article; zbMATH DE number 1054125