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  • Cited by 6
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Al-Omari, S. K. Q. 2013. Unified Treatment of the Krätzel Transformation for Generalized Functions. Abstract and Applied Analysis, Vol. 2013, p. 1.

    Roopkumar, R. 2007. Stieltjes transform for Boehmians. Integral Transforms and Special Functions, Vol. 18, Issue. 11, p. 845.

    Tröger, G. 1989. On the Iterated Stieltjes Transform of Generalized Functions. Mathematische Nachrichten, Vol. 141, Issue. 1, p. 129.

    Pilipović, Stevan 1987. Complex inversion formula for the distributional Stieltjes transform. Proceedings of the Edinburgh Mathematical Society, Vol. 30, Issue. 03, p. 363.

    Tröger, G. 1987. An Abelian and Tauberian theorem for the stieltjes transform of generalized functions. Czechoslovak Journal of Physics, Vol. 37, Issue. 9, p. 1061.

    Pilipović, Stevan 1986. An inversion theorem for the Stieltjes transform of distributions. Proceedings of the Edinburgh Mathematical Society, Vol. 29, Issue. 02, p. 171.

  • Proceedings of the Edinburgh Mathematical Society, Volume 20, Issue 1
  • March 1976, pp. 15-22

A distributional generalised Stieltjes transformation

  • R. S. Pathak (a1)
  • DOI:
  • Published online: 01 January 2009

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.

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(1) J. N. Pandey and A. H. Zemanian , Complex inversion for the generalized convolution transformation, Pacific J. Math. 25 (1968), 147157.

(4) D. B. Sumner , An inversion formula for the generalized Stieltjes transform, Bull. Amer. Math. Soc. 55 (1949), 174183.

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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