Multiresolution wavelet analysis of Bessel functions of scale $ν+1$

Abstract

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*-algebra O_{ν+1} arising from this multiresolution analysis.