Orthogonal series representations for generalized functions
type: Item
instance of: scholarly article
title: Orthogonal series representations for generalized functions
zbMATH Open document ID: 0647.46037
DOI: 10.1016/0022-247X(88)90308-3
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: The paper contains a theory of expansion of certain Schwartz distributions with respect to series of orthonormal families of functions in weighted \(L^ p\) spaces, i.e. \(A_{L_ wp}\) spaces. Conditions for convergence of orthogonal series in these spaces have been found. Also their dual spaces have been studied and characterized. The results include theorems on expansions into series of orthogonal polynomials, such as Hermite, Laguerre, Legendre etc. polynomials. The theory has applications, for instance, in solving some differential equations in distribution spaces.
Mathematics Subject Classification ID: 46F10
zbMATH DE Number: 4056318
zbMATH Keywords: expansion of certain Schwartz distributions with respect to series of orthonormal families of functions in weighted \(L^ p\) spaces
zbMATH Keywords: expansions into series of orthogonal polynomials
author: R. S. Pathak
reviewed by: Pawel Kruszynski
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4056318