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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| Format: | Article |
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Wiley
2018-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2018/6563823 |
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| author | Byung Keun Sohn |
| author_facet | Byung Keun Sohn |
| author_sort | Byung Keun Sohn |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-f0081e1a43dd4b8492bebf22742cad86 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f0081e1a43dd4b8492bebf22742cad862025-02-03T06:07:24ZengWileyInternational 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 |
| spellingShingle | Byung Keun Sohn Periodic Tempered Distributions of Beurling Type and Periodic Ultradifferentiable Functions with Arbitrary Support International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2018/6563823 |
| work_keys_str_mv | AT byungkeunsohn periodictempereddistributionsofbeurlingtypeandperiodicultradifferentiablefunctionswitharbitrarysupport |