Quasi-orthogonal decompositions of structured frames |
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Authors: | Massimo Fornasier |
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Institution: | NuHAG (Numerical Harmonic Analysis Group), Department of Mathematics, University of Vienna, Strudlhofgasse 4, A-1090 Wien, Austria |
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Abstract: | A decomposition of a Hilbert space into a quasi-orthogonal family of closed subspaces is introduced. We shall investigate conditions in order to derive bounded families of corresponding quasi-projectors or resolutions of the identity operator. Given a local family of atoms, or generalized stable basis, for each subspace, we show that the union of the local atoms can generate a global frame for the Hilbert space. Corresponding duals can be calculated in a flexible way by means of systems of quasi-projectors. An application to Gabor frames is presented as example of the use of this technique, for calculation of duals and explicit estimates of lattice constants. |
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Keywords: | Decomposition methods Frames Gabor analysis Iterative algorithms Wiener amalgams |
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