Shannon Multiresolution Analysis on the Heisenberg Group

TL;DR

This paper develops a multiresolution analysis framework on the Heisenberg group, introducing a sinc-type function and a wavelet example analogous to Shannon MRA, expanding wavelet theory to non-commutative groups.

Contribution

It introduces a novel notion of frame multiresolution analysis on the Heisenberg group and constructs a concrete wavelet example based on irreducible representations.

Findings

Defined a sinc-type function for the Heisenberg group

Constructed a wavelet FMRA analogous to Shannon MRA on 

Analyzed properties of the proposed multiresolution analysis

Abstract

We present a notion of frame multiresolution analysis on the Heisenberg group, abbreviated by FMRA, and study its properties. Using the irreducible representations of this group, we shall define a sinc-type function which is our starting point for obtaining the scaling function. Further, we shall give a concrete example of a wavelet FMRA on the Heisenberg group which is analogous to the Shannon MRA on $\RR$.