Shift generated dual frames for locally compact abelian groups (Q2890882)
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scientific article; zbMATH DE number 6045510
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Shift generated dual frames for locally compact abelian groups |
scientific article; zbMATH DE number 6045510 |
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12 June 2012
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frames
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Gramian operator
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locally compact abelian group
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shift invariant space
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SG-dual frame
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Shift generated dual frames for locally compact abelian groups (English)
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Let \(G\) be a metrizable, \(\sigma\)-compact locally compact abelian group with a compact open subgroup. In this paper the Gramian and the dual Gramian operators for shift invariant subspaces of \(L^2(G)\) are used for the characterization of shift generated dual frames for shift invariant spaces, which forms a frame for a subspace of \(L^2(G)\). Necessary and sufficient conditions for which a standard dual is a unique SG-dual frame of type I and type II are considered.
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