Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-25T13:03:21.672Z Has data issue: false hasContentIssue false
  • English
  • Français

On the infinitesimal generator of the Poisson operator

Published online by Cambridge University Press:  24 October 2008

G. O. Okikiolu
G. O. Okikiolu
Affiliation:
University of Sussex
Get access Rights & Permissions [Opens in a new window]

Extract

Throughout this paper we shall denote the space Lp(− ∞, ∞) by Lp, and the numbers p and p′ will be related by 1/p + 1/p′ = 1.

The Poisson operator Pa is defined by

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 4 , October 1966 , pp. 713 - 718
Copyright
Copyright © Cambridge Philosophical Society 1966

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Hille, E.On the generation of semi-groups and the theory of conjugate functions. Proc. R. Physiogr. Soc. Lund 21, 14 (1951), 130–142.Google Scholar
(2)Pollard, H.The semi-group property of Poisson transformation and Snow's inversion formula. Proc. American Math. Soc. 14 (1963), 285–290.Google Scholar
(3)Titchmarsh, E. C.The theory of Fourier integrals (Oxford, 1937).Google Scholar