Periodic Tempered Distributions of Beurling Type and Periodic Ultradifferentiable Functions with Arbitrary Support

Periodic Tempered Distributions of Beurling Type and Periodic Ultradifferentiable Functions with Arbitrary Support

Let Sω′(R) be the space of tempered distributions of Beurling type with test function space Sω(R) and let Eω,p be the space of ultradifferentiable functions with arbitrary support having a period p. We show that Eω,p is generated by Sω(R). Also, we show that the mapping Sω(R)→Eω,p is linear, onto, a...

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Main Author: Byung Keun Sohn
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2018/6563823
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spelling doaj-f0081e1a43dd4b8492bebf22742cad862020-11-24T22:32:42ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252018-01-01201810.1155/2018/65638236563823Periodic Tempered Distributions of Beurling Type and Periodic Ultradifferentiable Functions with Arbitrary SupportByung Keun Sohn0Department of Applied Mathematics, Inje University, Gimhae, Gyeongnam 50834, Republic of KoreaLet Sω′(R) be the space of tempered distributions of Beurling type with test function space Sω(R) and let Eω,p be the space of ultradifferentiable functions with arbitrary support having a period p. We show that Eω,p is generated by Sω(R). Also, we show that the mapping Sω(R)→Eω,p is linear, onto, and continuous and the mapping Sω,p′(R)→Eω,p′ is linear and onto where Sω,p′(R) is the subspace of Sω′(R) having a period p and Eω,p′ is the dual space of Eω,p.http://dx.doi.org/10.1155/2018/6563823
collection DOAJ
language English
format Article
sources DOAJ
author Byung Keun Sohn
spellingShingle Byung Keun Sohn
Periodic Tempered Distributions of Beurling Type and Periodic Ultradifferentiable Functions with Arbitrary Support
International Journal of Mathematics and Mathematical Sciences
author_facet Byung Keun Sohn
author_sort Byung Keun Sohn
title Periodic Tempered Distributions of Beurling Type and Periodic Ultradifferentiable Functions with Arbitrary Support
title_short Periodic Tempered Distributions of Beurling Type and Periodic Ultradifferentiable Functions with Arbitrary Support
title_full Periodic Tempered Distributions of Beurling Type and Periodic Ultradifferentiable Functions with Arbitrary Support
title_fullStr Periodic Tempered Distributions of Beurling Type and Periodic Ultradifferentiable Functions with Arbitrary Support
title_full_unstemmed Periodic Tempered Distributions of Beurling Type and Periodic Ultradifferentiable Functions with Arbitrary Support
title_sort periodic tempered distributions of beurling type and periodic ultradifferentiable functions with arbitrary support
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2018-01-01
description Let Sω′(R) be the space of tempered distributions of Beurling type with test function space Sω(R) and let Eω,p be the space of ultradifferentiable functions with arbitrary support having a period p. We show that Eω,p is generated by Sω(R). Also, we show that the mapping Sω(R)→Eω,p is linear, onto, and continuous and the mapping Sω,p′(R)→Eω,p′ is linear and onto where Sω,p′(R) is the subspace of Sω′(R) having a period p and Eω,p′ is the dual space of Eω,p.
url http://dx.doi.org/10.1155/2018/6563823
work_keys_str_mv AT byungkeunsohn periodictempereddistributionsofbeurlingtypeandperiodicultradifferentiablefunctionswitharbitrarysupport
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