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Generalized Frame Multiresolution Analysis of Abstract Hilbert Spaces

  • Manos Papadakis
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

We define a very generic class of multiresolution analysis of abstract Hilbert spaces. Their core subspaces have a frame produced by the action of an abelian unitary group on a countable frame multiscaling vector set, which may be infinite. We characterize all the associated frame multiwavelet vector sets and we generalize the concept of low and high pass filters. We also prove a generalization of the quadratic (conjugate) mirror filter condition, and we give two algorithms for the construction of the high pass filters associated to a given low pass filter.

Keywords

High Pass Filter Riesz Basis Dual Frame Frame Wavelet Range Projection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Science+Business Media New York 2004

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  • Manos Papadakis

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