Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-04T13:41:25.794Z Has data issue: false hasContentIssue false
  • English
  • Français

Note On a Stieltjes Type Of Inversion

Published online by Cambridge University Press:  20 November 2018

Pasquale Porcelli
Pasquale Porcelli*
Affiliation:
Illinois Institute of Technology, Chicago
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.

If F(z) is an analytic function for z ∉ [− ∞, −l],g(t) of bounded variation and real valued for 0 ≤ t ≤ 1 and

then the Stieltjes type of inversion between F(z) and g(t) (cf. 1, p. 339, Theorem 7a) is

where 0 ≤ v < u ≤ 1, ImF(z) is the imaginary part of F(z) and z = − t−l+iy.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 447 - 448
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Widder, D. V., The Laplace Transform, (Princeton, 1946).Google Scholar