Shannon-Like Wavelet Frames on a Class of Nilpotent Lie Groups

TL;DR

This paper constructs Shannon-like wavelet frames for certain nilpotent Lie groups using advanced mathematical theories, providing explicit bounds for their norms, which enhances understanding of wavelet analysis in non-commutative settings.

Contribution

It introduces a novel method to build Shannon-like wavelet frames on specific nilpotent Lie groups, combining representation, Fourier, and Gabor theories.

Findings

Constructed Shannon-like Parseval wavelet frames for the groups.

Computed an upper bound for the wavelet frame norms.

Extended wavelet frame theory to a new class of Lie groups.

Abstract

We prove and construct Shannon-like Parseval wavelet frames for a class of two step connected, and simply connected nilpotent Lie groups, using a mixture of representation theory, group Fourier theory, and Gabor theory. Moreover, we are able to compute an upperbound for the norm of these Parseval frame wavelets.