Multiresolution wavelet analysis of integer scale Bessel functions
Sergio Albeverio, Palle E.T. Jorgensen, Anna M. Paolucci

TL;DR
This paper develops a multiresolution wavelet framework for analyzing Bessel functions via Hilbert spaces, linking it to operator algebras, Markov chains, and quantum group representations.
Contribution
It introduces a novel multiresolution analysis for Bessel functions, connecting wavelet theory with operator algebras and quantum groups.
Findings
Identification of multiresolution subspaces for Bessel functions
Connection between wavelet analysis and $C^{st}$-algebra representations
Derivation of Markov traces for quantum groups
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 -algebra arising from this multiresolution analysis. A connection with Markov chains and representations of is found. Projection valued measures arising from the multiresolution analysis give rise to a Markov trace for quantum groups .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
