Global Symmetric Approximation of Frames
We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. Our proof relies on the geometric structure of the set of all Parseval frames q...
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2018
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/123376 |
| Aporte de: |
| id |
I19-R120-10915-123376 |
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| record_format |
dspace |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Inglés |
| topic |
Matemática Symmetric approximation Frame Hilbert space Hilbert–Schmidt operator Index of a pair of projections Partial isometry Löwdin orthogonalization |
| spellingShingle |
Matemática Symmetric approximation Frame Hilbert space Hilbert–Schmidt operator Index of a pair of projections Partial isometry Löwdin orthogonalization Chiumiento, Eduardo Hernán Global Symmetric Approximation of Frames |
| topic_facet |
Matemática Symmetric approximation Frame Hilbert space Hilbert–Schmidt operator Index of a pair of projections Partial isometry Löwdin orthogonalization |
| description |
We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. Our proof relies on the geometric structure of the set of all Parseval frames quadratically close to a given frame. In the process we show that its connected components can be parametrized by using the notion of index of a pair of projections, and we prove existence and uniqueness results of best approximation by Parseval frames restricted to these connected components. |
| format |
Articulo Articulo |
| author |
Chiumiento, Eduardo Hernán |
| author_facet |
Chiumiento, Eduardo Hernán |
| author_sort |
Chiumiento, Eduardo Hernán |
| title |
Global Symmetric Approximation of Frames |
| title_short |
Global Symmetric Approximation of Frames |
| title_full |
Global Symmetric Approximation of Frames |
| title_fullStr |
Global Symmetric Approximation of Frames |
| title_full_unstemmed |
Global Symmetric Approximation of Frames |
| title_sort |
global symmetric approximation of frames |
| publishDate |
2018 |
| url |
http://sedici.unlp.edu.ar/handle/10915/123376 |
| work_keys_str_mv |
AT chiumientoeduardohernan globalsymmetricapproximationofframes |
| bdutipo_str |
Repositorios |
| _version_ |
1764820449388134400 |