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- W2079862603 abstract "We construct a harmonic analysis of iteration systems which include those which arise from wavelet algorithms based on multiresolutions. While traditional discretizations lead to asymptotic formulas, we argue here for a direct Fourier duality; but it is based on a non - commutative harmonic analysis, specifically on representations of the Cuntz C* -algebras. With this approach the waling from the wavelet takes the form of an endomorphism of B(H), H a Hilbert space derived from the lattice of translations. We use this to describe, and to calculate, new invariants for the wavelets. those iteration systems which arise from wavelets and from Julia sets, we show that the associated endomorphisms are in fact Powers shifts." @default.
- W2079862603 created "2016-06-24" @default.
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- W2079862603 date "1999-01-01" @default.
- W2079862603 modified "2023-09-23" @default.
- W2079862603 title "Harmonic Analysis of Fractal Processes via C * - Algebras" @default.
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- W2079862603 doi "https://doi.org/10.1002/mana.19992000105" @default.
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