Existence of the best \(n\)-term approximants for structured dictionaries (Q444118)
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scientific article; zbMATH DE number 6065348
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of the best \(n\)-term approximants for structured dictionaries |
scientific article; zbMATH DE number 6065348 |
Statements
Existence of the best \(n\)-term approximants for structured dictionaries (English)
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13 August 2012
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The notion of uniform linear independence (ULI) for a dictionary in Hilbert spaces is introduced. It is shown that 1) the element of the \(n\)\,-term approximation exist for Bessel dictionaries which have ULI, 2) if a Bessel dictionary \(\Phi\) does note have ULI, then there exists an arbitrarily small pertubation of \(\Phi\) for which the best approximants do not exist. The obtained results are applied to frames.
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nonlinear approximation
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best approximations
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Bessel inequality
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frames
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