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On semi-groups of operators and the resolvents of their generators

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 (4) concerned with the study of ‘fundamental operators’, we have obtained results involving the resolvents of the generators of some semi-groups of operators in Lp (− ∞, ∞). In this paper we consider those results which, under suitable conditions, can be extended to cases where the resolvents do not necessarily form a class of fundamental operators. The main results of this type, given in Theorems 2·7 and 2·8, involve inequalities between members of the semi-group and the resolvent of the generators. The semi-groups to which the main results apply include those denned by the Poisson and the Gauss–Weierstrass operators.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 3 , November 1969 , pp. 533 - 540
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

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