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On the infinitesimal generator of the Poisson operator II. The n-dimensional case

Published online by Cambridge University Press:  24 October 2008

G. O. Okikiolu
G. O. Okikiolu
Affiliation:
University of East Anglia
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Extract

In a recent paper (5) the author gave an alternative proof of the result due to Hille(2) for the representation of the infinitesimal generator of the Poisson operator. In this paper we obtain the n-dimensional analogue of the result by using arguments similar to those employed in (5).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 1021 - 1025
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Calderon, A. P. and Zygmund, A.On the existence of certain singular integrals. Acta. Math. 88 (1952), 85–139.CrossRefGoogle Scholar
(2)Hille, E.On the generator of semi-groups and the theory of conjugate functions. Proc. Roy. Physiog. Soc. Lund. 21 (1951), 130–142.Google Scholar
(3)Hille, E. and Phillips, R. S.Functional analysis and semi-groups (Providence, R. I., 1957).Google Scholar
(4)Horvàth, J.Sur les fonctions conjugèes a plusieurs variables. Nederl. Akad. Wetensch. Proc. Ser. A 15 (1953), 17–29.CrossRefGoogle Scholar
(5)Okikiolu, G. O.On the infinitesimal generator of the Poisson operator, Proc. Cambridge Philos. Soc. 62 (1966), 713–718.CrossRefGoogle Scholar
(6)Yosida, K.Functional analysis (Berlin, 1965).Google Scholar