On Some Sampling-Related Frames in U-Invariant Spaces
This paper is concerned with the characterization as frames of some sequences in U-invariant spaces of a separable Hilbert space ℋ where U denotes an unitary operator defined on ℋ; besides, the dual frames having the same form are also found. This general setting includes, in particular, shift-invar...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/761620 |
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| author | H. R. Fernández-Morales A. G. García M. A. Hernández-Medina M. J. Muñoz-Bouzo |
| author_facet | H. R. Fernández-Morales A. G. García M. A. Hernández-Medina M. J. Muñoz-Bouzo |
| author_sort | H. R. Fernández-Morales |
| collection | DOAJ |
| description | This paper is concerned with the characterization as frames of some sequences in U-invariant spaces of a separable Hilbert space ℋ where U denotes an unitary operator defined on ℋ; besides, the dual frames having the same form are also found. This general setting includes, in particular, shift-invariant or modulation-invariant subspaces in L2ℝ, where these frames are intimately related to the generalized sampling problem. We also deal with some related perturbation problems. In doing so, we need the unitary operator U to belong to a continuous group of unitary operators. |
| format | Article |
| id | doaj-art-6ddb7a4718b546b7824046c900c8018c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6ddb7a4718b546b7824046c900c8018c2025-02-03T01:33:13ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/761620761620On Some Sampling-Related Frames in U-Invariant SpacesH. R. Fernández-Morales0A. G. García1M. A. Hernández-Medina2M. J. Muñoz-Bouzo3Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés-Madrid, SpainDepartamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés-Madrid, SpainDepartamento de Matemáticas Aplicada, E.T.S.I.T., U.P.M., Avda. Complutense 30, 28040 Madrid, SpainDepartamento de Matemáticas Fundamentales, Facultad de Ciencias, U.N.E.D. Senda del Rey 9, 28040 Madrid, SpainThis paper is concerned with the characterization as frames of some sequences in U-invariant spaces of a separable Hilbert space ℋ where U denotes an unitary operator defined on ℋ; besides, the dual frames having the same form are also found. This general setting includes, in particular, shift-invariant or modulation-invariant subspaces in L2ℝ, where these frames are intimately related to the generalized sampling problem. We also deal with some related perturbation problems. In doing so, we need the unitary operator U to belong to a continuous group of unitary operators.http://dx.doi.org/10.1155/2013/761620 |
| spellingShingle | H. R. Fernández-Morales A. G. García M. A. Hernández-Medina M. J. Muñoz-Bouzo On Some Sampling-Related Frames in U-Invariant Spaces Abstract and Applied Analysis |
| title | On Some Sampling-Related Frames in U-Invariant Spaces |
| title_full | On Some Sampling-Related Frames in U-Invariant Spaces |
| title_fullStr | On Some Sampling-Related Frames in U-Invariant Spaces |
| title_full_unstemmed | On Some Sampling-Related Frames in U-Invariant Spaces |
| title_short | On Some Sampling-Related Frames in U-Invariant Spaces |
| title_sort | on some sampling related frames in u invariant spaces |
| url | http://dx.doi.org/10.1155/2013/761620 |
| work_keys_str_mv | AT hrfernandezmorales onsomesamplingrelatedframesinuinvariantspaces AT aggarcia onsomesamplingrelatedframesinuinvariantspaces AT mahernandezmedina onsomesamplingrelatedframesinuinvariantspaces AT mjmunozbouzo onsomesamplingrelatedframesinuinvariantspaces |