Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T01:13:44.911Z Has data issue: false hasContentIssue false
  • English
  • Français

A distributional generalised Stieltjes transformation

Published online by Cambridge University Press:  20 January 2009

R. S. Pathak
R. S. Pathak
Affiliation:
Banaras Hindu University, Varanasi 221005, India
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The generalised Stieltjes transform of a function f(t) ∈ L(0, ∞) is defined by

The integral converges for complex s in the region Ω, where Ω is the s-plane cut from the origin along the negative real axis.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 20 , Issue 1 , March 1976 , pp. 15 - 22
Copyright
Copyright © Edinburgh Mathematical Society 1976

References

REFERENCES

(1) Pandey, J. N. and Zemanian, A. H., Complex inversion for the generalized convolution transformation, Pacific J. Math. 25 (1968), 147–157.CrossRefGoogle Scholar
(2) Pandey, J. N., On the Stieltjes transform of generalized functions, Proc. Cambridge Philos. Soc. 71 (1972), 85–96.CrossRefGoogle Scholar
(3) Pollard, H., Studies on the Stieltjes transform, Dissertation,Google Scholar
Harvard, , Bull. Amer. Math. Soc. 48 (1942), 214.Google Scholar
(4) Sumner, D. B., An inversion formula for the generalized Stieltjes transform, Bull. Amer. Math. Soc. 55 (1949), 174–183.Google Scholar
(5) Tttchmarsh, E. C., Theory of functions, 2nd edition (Oxford Univ. Press, 1939).Google Scholar
(6) Widder, D. V., The Laplace transform (Princeton, 1946).Google Scholar
(7) Zemanian, A. H., Generalized integral transformations (Interscience Publishers, 1968).Google Scholar