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Titlebook: Excursions in Harmonic Analysis, Volume 2; The February Fourier Travis D. Andrews,Radu Balan,Kasso A. Okoudjou Book 2013 Springer Science+B

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Positive-Operator-Valued Measures: A General Setting for Framesrable Hilbert space and the theory of frames on that space, including its most important generalizations. The concept of a framed POVM is introduced, and classical frames, fusion frames, generalized frames, and other variants of frames are all shown to arise as framed POVMs. This observation allows
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Extending Wavelet Filters: Infinite Dimensions, the Nonrational Case, and Indefinite Inner Product Savelets, in signal processing, and in systems, we here expand the framework. Motivated by applications and by bringing to bear tools from reproducing kernel theory, we point out the role of non-positive definite Hermitian inner products (negative squares), for example, Krein spaces, in the study of
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Parametric Optimization of Biorthogonal Wavelets and Filterbanks via Pseudoframes for Subspacesudoframe sequences need not reside within the subspace of interest. In particular, when PFFS is applied to biorthogonal wavelets, the underlying flexibility presents opportunities to incorporate optimality, regularity, as well as perfect reconstruction into one parametric design approach. This appro
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