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Abelian theorems for the distributional Stieltjes transformation

Published online by Cambridge University Press:  24 October 2008

Jean Lavoine  and
O. P. Misra
Jean Lavoine
Affiliation:
C.N.R.S., 17 Rue Vérollot F 94800 Villejuif, France
O. P. Misra
Affiliation:
Indian Institute of Technology, New Delhi
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Extract

0. Introduction. Asymptotic behaviour of distributions (Silva(8) and Benedetto (l)) plays a fundamental role in the analysis of singularities of generalized integral transforms. Such analysis in terms of Abelian theorems for the distributional Stieltjes transformation has been obtained by Misra (6) and Lavoine and Misra (3). To obtain his results Misra used some Abelian theorems (see Misra (6), theorems 3·1·1 and 4·1·1) for the Stieltjes transformation of functions which were essentially generalizations of the results given by Widder (9), pp. 183–185. The object of the present paper is to complete the work given by the authors in (3); Sections 2 and 3 of this paper are devoted to obtaining Abelian theorems concerning the distributional Stieltjes transformation in terms of the behaviour of this transform near the origin and at infinity.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 2 , September 1979 , pp. 287 - 294
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

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