Paley-Wiener description of K-spherical Besov spaces on the Heisenberg group

TL;DR

This paper characterizes K-spherical Besov spaces on the Heisenberg group using bandlimited wavelet coefficients and spherical Fourier transforms, advancing the understanding of harmonic analysis on non-commutative groups.

Contribution

It introduces a novel approach to characterize Besov spaces via compactly supported admissible functions in abstract Hilbert spaces, specifically applied to the Heisenberg group.

Findings

Characterization of Besov spaces using bandlimited wavelet coefficients.

Development of an approach for Besov space characterization in abstract Hilbert spaces.

Application of spherical Fourier transform to non-commutative harmonic analysis.

Abstract

We characterize the Besov spaces associated to the Gelfand pairs on the Heisenberg group. The characterization is given in terms of bandlimited wavelet coefficients where the bandlimitedness is introduced using spherical Fourier transform. To obtain these results we develop an approach to the characterization of Besov spaces in abstract Hilbert spaces through compactly supported admissible functions.