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A note on the distributional Stieltjes transformation

Published online by Cambridge University Press:  24 October 2008

Arpad Takači
Arpad Takači
Affiliation:
Institute of Mathematics, Novi Sad, Yugoslavia
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Extract

In this note we use the notion of the quasiasymptotic behaviour of distributions (introduced in [2]) in order to obtain a final value Abelian theorem for the distributional Stieltjes transformation. At the end of the note we give a few examples in which two different concepts of the asymptotic behaviour of distributions are compared.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 3 , November 1983 , pp. 523 - 527
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

[1] Carmichael, R. D. and Milton, E. O.. Abelian Theorems for the distributional Stieltjes transform. J. Math. Anal. Appl. 72 (1979), 195–205.Google Scholar
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[3] Drožžinov, Ju. N. and Zav´Jalov, B. I.. Tauberian theorems for generalized functions with supports in a cone (in Russian). Mat. Sb. 108 (1979) 78–90.Google Scholar
[4] Lavione, J. and Misra, O. P.. Théorémes abéliens pour la transformation de Stieltjes des distributions. C. R. Acad. Sci. Paria, Série A 279 (1974), 99–102.Google Scholar
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[6] Lavoine, J. and Misra, O. P.. Sur la transformation de Stieltjes des distributions et son inversion au moyen de la transformation de Laplace. C. R. Acad. Sci. Paris, Série A 290 (1980), 139–142.Google Scholar