On a family of weighted convolution algebras
Continuing a line of research initiated by Larsen, Liu and Wang [12], Martin and Yap [13], Gürkanli [15], and influenced by Reiter's presentation of Beurling and Segal algebras in Reiter [2,10] this paper presents the study of a family of Banach ideals of Beurling algebras Lw1(G), G a locally c...
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| Format: | Article |
| Language: | English |
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Wiley
1990-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171290000758 |
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| author | Hans G. Feichtinger A. Turan Gürkanli |
| author_facet | Hans G. Feichtinger A. Turan Gürkanli |
| author_sort | Hans G. Feichtinger |
| collection | DOAJ |
| description | Continuing a line of research initiated by Larsen, Liu and Wang [12], Martin and Yap [13], Gürkanli [15], and influenced by Reiter's presentation of Beurling and Segal algebras in Reiter [2,10] this paper presents the study of a family of Banach ideals of Beurling algebras Lw1(G), G a locally compact Abelian group. These spaces are defined by weighted Lp-conditions of their Fourier transforms. In the first section invariance properties and asymptotic estimates for the translation and modulation operators are given. Using these it is possible to characterize inclusions in section 3 and to show that two spaces of this type coincide if and only if their parameters are equal. In section 4 the existence of approximate identities in these algebras is established, from which, among other consequences, the bijection between the closed ideals of these algebras and those of the corresponding Beurling algebra is derived. |
| format | Article |
| id | doaj-art-bd7ec464af20465a94c774ad3ba7ae33 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1990-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-bd7ec464af20465a94c774ad3ba7ae332025-02-03T01:02:58ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113351752510.1155/S0161171290000758On a family of weighted convolution algebrasHans G. Feichtinger0A. Turan Gürkanli1Institut für Mathematik, Universiät Wien, Strudlhofgasse 4, Wien A-1090, AustriaOndokuz Mayis University, Faculty of Art and Sciences, Department of Mathematics, Samsun, TurkeyContinuing a line of research initiated by Larsen, Liu and Wang [12], Martin and Yap [13], Gürkanli [15], and influenced by Reiter's presentation of Beurling and Segal algebras in Reiter [2,10] this paper presents the study of a family of Banach ideals of Beurling algebras Lw1(G), G a locally compact Abelian group. These spaces are defined by weighted Lp-conditions of their Fourier transforms. In the first section invariance properties and asymptotic estimates for the translation and modulation operators are given. Using these it is possible to characterize inclusions in section 3 and to show that two spaces of this type coincide if and only if their parameters are equal. In section 4 the existence of approximate identities in these algebras is established, from which, among other consequences, the bijection between the closed ideals of these algebras and those of the corresponding Beurling algebra is derived.http://dx.doi.org/10.1155/S0161171290000758Beurling algebraweighted Lp-spacesconvolutionideal theoremBanach idealsfactorization. |
| spellingShingle | Hans G. Feichtinger A. Turan Gürkanli On a family of weighted convolution algebras International Journal of Mathematics and Mathematical Sciences Beurling algebra weighted Lp-spaces convolution ideal theorem Banach ideals factorization. |
| title | On a family of weighted convolution algebras |
| title_full | On a family of weighted convolution algebras |
| title_fullStr | On a family of weighted convolution algebras |
| title_full_unstemmed | On a family of weighted convolution algebras |
| title_short | On a family of weighted convolution algebras |
| title_sort | on a family of weighted convolution algebras |
| topic | Beurling algebra weighted Lp-spaces convolution ideal theorem Banach ideals factorization. |
| url | http://dx.doi.org/10.1155/S0161171290000758 |
| work_keys_str_mv | AT hansgfeichtinger onafamilyofweightedconvolutionalgebras AT aturangurkanli onafamilyofweightedconvolutionalgebras |