Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 6
  • Cited by
    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: http://dx.doi.org/10.1017/S0013091500015716
  • Published online: 01 January 2009
Abstract

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.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      A distributional generalised Stieltjes transformation
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      A distributional generalised Stieltjes transformation
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      A distributional generalised Stieltjes transformation
      Available formats
      ×
Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

(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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×