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: |
| Sumario: | 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. |
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