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A tauberian theorem related to the modified Hankel transform

Published online by Cambridge University Press:  17 April 2009

Kusum Soni  and
R.P. Soni
Kusum Soni
Affiliation:
Department of Mathematics, University of Tennessee, Knoxvilie, Tennessee, USA.
R.P. Soni
Affiliation:
Department of Mathematics, University of Tennessee, Knoxvilie, Tennessee, USA.
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Abstract

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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.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 2 , October 1974 , pp. 167 - 180
Copyright
Copyright © Australian Mathematical Society 1974

References

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