Continuity of the fractional Hankel wavelet transform on the spaces of type S

TL;DR

This paper investigates the continuity properties of the fractional Hankel transform and its wavelet transform on Gel'fand-Shilov and ultradifferentiable function spaces, extending understanding of their mathematical behavior.

Contribution

It establishes the continuity of fractional Hankel and wavelet transforms on specific function spaces, advancing theoretical knowledge in harmonic analysis.

Findings

Proves continuity of fractional Hankel transform on Gel'fand-Shilov spaces

Demonstrates continuity of fractional Hankel wavelet transform on these spaces

Extends results to ultradifferentiable function spaces

Abstract

In this article we study the fractional Hankel transform and its inverse on certain Gel'fand-Shilov spaces of type S. The continuous fractional wavelet transform is defined involving the fractional Hankel transform. The continuity of fractional Hankel wavelet transform is discussed on Gel'fand-Shilov spaces of type S. This article goes further to discuss the continuity property of fractional Hankel transform and fractional Hankel wavelet transform on the ultradifferentiable function spaces.