The Zak transform and the structure of spaces invariant by the action of an LCA group
We study closed subspaces of L2(X), where (X,μ) is a σ-finite measure space, that are invariant under the unitary representation associated to a measurable action of a discrete countable LCA group Γ on X. We provide a complete description for these spaces in terms of range functions and a suitable g...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00221236_v269_n5_p1327_Barbieri |
| Aporte de: |
| id |
todo:paper_00221236_v269_n5_p1327_Barbieri |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_00221236_v269_n5_p1327_Barbieri2023-10-03T14:27:18Z The Zak transform and the structure of spaces invariant by the action of an LCA group Barbieri, D. Hernández, E. Paternostro, V. Frames LCA groups Shift-invariant spaces Zak transform We study closed subspaces of L2(X), where (X,μ) is a σ-finite measure space, that are invariant under the unitary representation associated to a measurable action of a discrete countable LCA group Γ on X. We provide a complete description for these spaces in terms of range functions and a suitable generalized Zak transform. As an application of our main result, we prove a characterization of frames and Riesz sequences in L2(X) generated by the action of the unitary representation under consideration on a countable set of functions in L2(X). Finally, closed subspaces of L2(G), for G being an LCA group, that are invariant under translations by elements on a closed subgroup Γ of G are studied and characterized. The results we obtain for this case are applicable to cases where those already proven in [5,7] are not. © 2015 Elsevier Inc. Fil:Paternostro, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00221236_v269_n5_p1327_Barbieri |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Frames LCA groups Shift-invariant spaces Zak transform |
| spellingShingle |
Frames LCA groups Shift-invariant spaces Zak transform Barbieri, D. Hernández, E. Paternostro, V. The Zak transform and the structure of spaces invariant by the action of an LCA group |
| topic_facet |
Frames LCA groups Shift-invariant spaces Zak transform |
| description |
We study closed subspaces of L2(X), where (X,μ) is a σ-finite measure space, that are invariant under the unitary representation associated to a measurable action of a discrete countable LCA group Γ on X. We provide a complete description for these spaces in terms of range functions and a suitable generalized Zak transform. As an application of our main result, we prove a characterization of frames and Riesz sequences in L2(X) generated by the action of the unitary representation under consideration on a countable set of functions in L2(X). Finally, closed subspaces of L2(G), for G being an LCA group, that are invariant under translations by elements on a closed subgroup Γ of G are studied and characterized. The results we obtain for this case are applicable to cases where those already proven in [5,7] are not. © 2015 Elsevier Inc. |
| format |
JOUR |
| author |
Barbieri, D. Hernández, E. Paternostro, V. |
| author_facet |
Barbieri, D. Hernández, E. Paternostro, V. |
| author_sort |
Barbieri, D. |
| title |
The Zak transform and the structure of spaces invariant by the action of an LCA group |
| title_short |
The Zak transform and the structure of spaces invariant by the action of an LCA group |
| title_full |
The Zak transform and the structure of spaces invariant by the action of an LCA group |
| title_fullStr |
The Zak transform and the structure of spaces invariant by the action of an LCA group |
| title_full_unstemmed |
The Zak transform and the structure of spaces invariant by the action of an LCA group |
| title_sort |
zak transform and the structure of spaces invariant by the action of an lca group |
| url |
http://hdl.handle.net/20.500.12110/paper_00221236_v269_n5_p1327_Barbieri |
| work_keys_str_mv |
AT barbierid thezaktransformandthestructureofspacesinvariantbytheactionofanlcagroup AT hernandeze thezaktransformandthestructureofspacesinvariantbytheactionofanlcagroup AT paternostrov thezaktransformandthestructureofspacesinvariantbytheactionofanlcagroup AT barbierid zaktransformandthestructureofspacesinvariantbytheactionofanlcagroup AT hernandeze zaktransformandthestructureofspacesinvariantbytheactionofanlcagroup AT paternostrov zaktransformandthestructureofspacesinvariantbytheactionofanlcagroup |
| _version_ |
1782027995629748224 |