On Hankel Transform and Hankel Convolution of Beurling Type Distributions Having Upper Bounded Support

A Generalized Hankel Convolution on Zemanian Spaces

We define a new generalized Hankel convolution on the Zemanian distribution spaces of slow growth.

The Hankel transform

Calderón's reproducing formula for Hankel convolution

where φ :Rn → C and φt(x)= t−nφ(x/t), t > 0. For conditions of validity of identity (1.1), we may refer to [3]. Hankel convolution introduced by Hirschman Jr. [5] related to the Hankel transform was studied at length by Cholewinski [1] and Haimo [4]. Its distributional theory was developed byMarrero and Betancor [6]. Pathak and Pandey [8] used Hankel convolution in their study of pseudodifferen...

Transformations Preserving the Hankel Transform

Transformations Preserving the Hankel Transform Christopher French Department of Mathematics and Statistics Grinnell College Grinnell, IA 50112 USA [email protected] Abstract We classify all polynomial transformations of integer sequences which preserve the Hankel transform, thus generalizing examples due to Layman and Spivey & Steil. We also show that such transformations form a group ...

On a generalized finite Hankel transform

In the present work we introduce a finite integral transform involving combination of Bessel functions as kernel under prescribed conditions. The corresponding inversion formula and some properties of this transform have also been given. Three problems of heat conduction in an infinite, a semi-infinite and a finite circular cylinder bounded by given surfaces with radiation-type boundary value c...