Multiresolution wavelet analysis of integer scale Bessel functions

Details Multiresolution wavelet analysis of integer scale Bessel functions Multiresolution wavelet analysis of integer scale Bessel functions

2007-05-15

arxiv.org/abs/0705.2188v2

Mathematics

Representation Theory

Research paper, 32 pages

Scientific paper

10.1063/1.2750291

We identify multiresolution subspaces giving rise via Hankel transforms to Bessel functions. They emerge as orthogonal systems derived from geometric Hilbert-space considerations, the same way the wavelet functions from a multiresolution scaling wavelet construction arise from a scale of Hilbert spaces. We study the theory of representations of the $C^{\ast}$-algebra $% O_{\nu +1}$ arising from this multiresolution analysis. A connection with Markov chains and representations of $O_{\nu +1}$ is found. Projection valued measures arising from the multiresolution analysis give rise to a Markov trace for quantum groups $SO_q$.

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