Wiener Tauberian theorems for vector-valued functions
Different versions of Wiener's Tauberian theorem are discussed for the generalized group algebra L1(G,A) (of integrable functions on a locally compact abelian group G taking values in a commutative semisimple regular Banach algebra A) using A-valued Fourier transforms. A weak form of Wiener...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171294000694 |
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| _version_ | 1850158771585679360 |
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| author | K. Parthasarathy Sujatha Varma |
| author_facet | K. Parthasarathy Sujatha Varma |
| author_sort | K. Parthasarathy |
| collection | DOAJ |
| description | Different versions of Wiener's Tauberian theorem are discussed for the generalized group algebra L1(G,A) (of integrable functions on a locally compact abelian group G taking values in a commutative semisimple regular Banach algebra A) using A-valued Fourier transforms. A weak form of Wiener's Tauberian property is introduced and it is proved that L1(G,A) is weakly Tauberian if and only if A is. The vector analogue of Wiener's L2-span of translates theorem is examined. |
| format | Article |
| id | doaj-art-665a5b8ee22f49cc877132de65c810dd |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-665a5b8ee22f49cc877132de65c810dd2025-08-20T02:23:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117347547810.1155/S0161171294000694Wiener Tauberian theorems for vector-valued functionsK. Parthasarathy0Sujatha Varma1Ramanujan Institute, University of Madras, Madras 600 005, IndiaSchool of Sciences, Indira Gandhi National Open University, New Delhi 110 068, IndiaDifferent versions of Wiener's Tauberian theorem are discussed for the generalized group algebra L1(G,A) (of integrable functions on a locally compact abelian group G taking values in a commutative semisimple regular Banach algebra A) using A-valued Fourier transforms. A weak form of Wiener's Tauberian property is introduced and it is proved that L1(G,A) is weakly Tauberian if and only if A is. The vector analogue of Wiener's L2-span of translates theorem is examined.http://dx.doi.org/10.1155/S0161171294000694generalized group algebraWiener's Tauberian property. |
| spellingShingle | K. Parthasarathy Sujatha Varma Wiener Tauberian theorems for vector-valued functions International Journal of Mathematics and Mathematical Sciences generalized group algebra Wiener's Tauberian property. |
| title | Wiener Tauberian theorems for vector-valued functions |
| title_full | Wiener Tauberian theorems for vector-valued functions |
| title_fullStr | Wiener Tauberian theorems for vector-valued functions |
| title_full_unstemmed | Wiener Tauberian theorems for vector-valued functions |
| title_short | Wiener Tauberian theorems for vector-valued functions |
| title_sort | wiener tauberian theorems for vector valued functions |
| topic | generalized group algebra Wiener's Tauberian property. |
| url | http://dx.doi.org/10.1155/S0161171294000694 |
| work_keys_str_mv | AT kparthasarathy wienertauberiantheoremsforvectorvaluedfunctions AT sujathavarma wienertauberiantheoremsforvectorvaluedfunctions |