Radial Multiresolution, Cuntz Algebras Representations and an Application to Fractals |
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Authors: | Sergio Albeverio Anna Maria Paolucci |
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Institution: | 1. Institut für Angewandte Mathematik, Universit?t Bonn, Wegelerstr. 6, D-53115, Bonn, Germany 2. SFB 611, Bonn, BiBos (Bielefeld-Bonn), IZKS Bonn, CERFIM (Locarno) and ACC. ARCH (USI), Bonn, Switzerland 3. Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111, Bonn, Germany
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Abstract: | We study Bernoulli type convolution measures on attractor sets arising from iterated function systems on R. In particular we examine orthogonality for Hankel frequencies in the Hilbert space of square integrable functions on the
attractor coming from a radial multiresolution analysis on R3. A class of fractals emerges from a finite system of contractive affine mappings on the zeros of Bessel functions. We have
then fractal measures on one hand and the geometry of radial wavelets on the other hand. More generally, multiresolutions
serve as an operator theoretic framework for the study of such selfsimilar structures as wavelets, fractals, and recursive
basis algorithms. The purpose of the present paper is to show that this can be done for a certain Bessel–Hankel transform.
Submitted: February 20, 2008., Accepted: March 6, 2008. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 42C40 37G99 43A32 46E22 43A62 47C15 |
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