ON HANKEL TYPE CONVOLUTION OPERATORS
By
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
Abstract
Let H′α,β be the Zemanian type space of Hankel transformable generalised functions and let O′α,β,* be the space of Hankel convolution operators for H′α,β . This H′α,β is the dual of a subspace H′α,β of O′α,β,* for which O′α,β,* is also the space of Hankel convolution. In this paper the elements of O′α,β,* are characterised as those in L(Hα,β) and in L(H′α,β) that commute with Hankel translations. Moreover, necessary and sufficient condition on the generalised Hankel type transform h′α,βS of S ∈ O′α,β,* are established in order that every T ∈ O′α,β,* such that S ∗ T ∈ Hα,β lie in H′α,β.
2020 Mathematical Sciences Classification: 46F12
Keywords and Phrases: Generalized functions, Hankel type transformation, Hankel type translation, Hankel type convolution.