Some Versions of Beurling's Theorem on H-type Groups

TL;DR

This paper extends Beurling's theorem to H-type groups by establishing Gutzmer's formula and using the modified Radon transform, broadening the theorem's applicability in harmonic analysis on these groups.

Contribution

It introduces new versions of Beurling's theorem on H-type groups through the development of Gutzmer's formula and the modified Radon transform techniques.

Findings

Established Gutzmer's formula for H-type groups

Proved analogues of Beurling's theorem on H-type groups

Derived multiple versions of the theorem using Radon transform

Abstract

We prove an analogue of Beurling's theorem on the H-type groups of certain dimensions after establishing the Gutzmer's formula for the H-type groups. We also obtain some other versions of the theorem using the modified Radon transform.