Abelian and Tauberian results for the fractional Hankel transform in Zemanian-type spaces

TL;DR

This paper develops new Abelian and Tauberian theorems for the fractional Hankel transform within Zemanian-type spaces, including the construction of a novel space with the largest known distribution dual, advancing the theoretical understanding of FrHT.

Contribution

It introduces a new Zemanian-type space as a projective limit, proving it has the Montel property, and establishes new Abelian and Tauberian results for the fractional Hankel transform in this setting.

Findings

Established Abelian-type theorem for FrHT in Zemanian spaces

Constructed a new Zemanian-type space with Montel property

Proved new Abelian and Tauberian theorems for FrHT in the extended space

Abstract

In this paper, we first present an Abelian-type theorem for the fractional Hankel transform (FrHT) within Zemanian generalized function spaces. To prove this, we show that these spaces have the Montel property. Next, we construct a new Zemanian-type space as a projective limit of suitable Banach spaces. Its dual is the largest known distribution space admitting the FrHT. Finally, within this extended setting, we establish new Abelian and Tauberian-type results for the FrHT.