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

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.