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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
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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

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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