Spectral analysis and synthesis on symmetric spaces
type: Item
instance of: scholarly article
title: Spectral analysis and synthesis on symmetric spaces
zbMATH Open document ID: 0647.43004
DOI: 10.1016/0022-247X(87)90137-5
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: The starting point of this paper is the Schwarz theorem which states that every non-trivial closed and translation-invariant subspace V of the space \(C^{\infty}(R)\) of smooth functions on the real line contains some function of the form \(p(x)e^{qx}\), where p(.) is a polynomial and q a complex number and moreover that the space V is spanned by such functions. The author studies the problem of Schwarz in the space \(C^{\infty}(X)\), where X is a rank one symmetric space of non-compact type and proves that the spectral analysis and synthesis hold for those invariant subspaces of \(C^{\infty}(X)\) whose spectrum does not contain the zeroes of the Harish-Chandra function c.
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 4056268
zbMATH Keywords: Schwarz theorem
zbMATH Keywords: translation-invariant subspace
zbMATH Keywords: rank one symmetric space
zbMATH Keywords: spectral analysis
zbMATH Keywords: synthesis
zbMATH Keywords: Harish-Chandra function
author: Antoni Wawrzyńczyk
MaRDI profile type: Publication
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full work available at URL: 0022-247x(87)90137-5
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description: scientific article; zbMATH DE number 4056268