Generalized exponential series for distributions
type: Item
instance of: scholarly article
title: Generalized exponential series for distributions
zbMATH Open document ID: 0893.30003
published in: Doklady Mathematics
publication date: 1998-07-23T00:00:00Z
review text: Absolutely representing systems of generalized exponentials are considered which admit nontrivial expansions of zero in the space \(D_{\beta}'([-a,a]^p)\) of distributions on the \(p\)-dimensional cube \([-a,a]^p .\) The author finds conditions under which the existence of a nontrivial expansion of zero in a system of generalized exponentials \(\mathcal E_{\Lambda} \) that is absolutely convergent in \(D_{\beta}'([-a,a]^p)\) imply that \(\mathcal E_{\Lambda} \) is an absolutely representing system in \(D_{\beta}'([-a,a]^p).\) He also deals with the problem of existence of a continuous linear right inverse of the representation operator associated to an absolutely representing system \(\mathcal E_{\Lambda} \) of generalized exponentials.
Mathematics Subject Classification ID: 30B50
Mathematics Subject Classification ID: 46A35
zbMATH DE Number: 1113119
zbMATH Keywords: representing systems
zbMATH Keywords: generalized exponentials
zbMATH Keywords: right inverse
author: Sergej N. Melikhov
reviewed by: Fritz Haslinger
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1113119