Approximation of the Inverse Frame Operator and Applications to Gabor Frames |
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Authors: | Peter G. Casazza Ole Christensen |
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Affiliation: | Department of Mathematics, University of Missouri, Columbia, Missouri, 65211, U.S.A.f1;Department of Mathematics, Technical University of Denmark, 2800, Lyngby, Denmark, f2 |
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Abstract: | A frame allows every element in a Hilbert space to be written as a linear combination of the frame elements, with coefficients called frame coefficients. Calculation of the frame coefficients requires inversion of an operator S on . We show how the inverse of S can be approximated as close as we like using finite-dimensional linear algebra. In contrast with previous methods, our approximation can be used for any frame. Various consequences for approximation of the frame coefficients or approximation of the solution to a moment problem are discussed. We also apply the results to Gabor frames and frames consisting of translates of a single function. |
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