Bulletin of the Australian Mathematical Society

Table of Contents - 1974 - Volume 11, Issue 02  

Research Article

A tauberian theorem related to the modified Hankel transform

Kusum Sonia1 and R.P. Sonia1

a1 Department of Mathematics, University of Tennessee, Knoxvilie, Tennessee, USA.

Abstract

The modified Hankel transform arises naturally in connection with certain semigroup operations on measures in probability theory. We give a tauberian theorem for this transform when certain higher moments exist. The probabilistic significance of our result is that it translates a regularity condition on the transform into a direct condition on the measure. This complements earlier results by Pitman and Bingham for the trigonometric and the modified Hankel transform respectively.

(Received April 17 1974)