B. B. Waphare1, R. Z. Shaikh1 and N. M. Rane2

1Department of Mathematics, MAEER’s MIT Arts, Commerece & Science College

Alandi(D), Pune-412105, Maharastra, India.

2Avantika University, Ujjain-456006, Madhya Pradesh, India.

Email: balasahebwaphare@gmail.com, shaikhrahilanaz@gmail.com, nitin@avantika.edu.in

(Received : May 31, 2022; In front : July 30, 2022; Accepted : October 17, 2022)

DOI: https://doi.org/10.58250/jnanabha.2022.52218


Let Hα,β be the Zemanian type space of Hankel transformable generalised functions and let Oα,β,* be the space of Hankel convolution operators for Hα,β . This Hα,β is the dual of a subspace Hα,β of Oα,β,*  for which Oα,β,* is also the space of Hankel convolution. In this paper the elements of Oα,β,*  are characterised as those in L(Hα,β) and in L(Hα,β) that commute with Hankel translations. Moreover, necessary and sufficient condition on the generalised Hankel type transform hα,βS of S ∈ Oα,β,* are established in order that every TOα,β,* such that S ∗ T ∈ Hα,β lie in Hα,β.

2020 Mathematical Sciences Classification: 46F12

Keywords and Phrases: Generalized functions, Hankel type transformation, Hankel type translation, Hankel type convolution.

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