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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A generalized domain for semigroup generators


Author: Michael G. Crandall
Journal: Proc. Amer. Math. Soc. 37 (1973), 434-440
MSC: Primary 47D05; Secondary 47H99
MathSciNet review: 0313873
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Abstract: A generalized domain $ \hat D(A)$ is assigned to a certain class of generators A of semigroups of nonlinear transformations S on Banach spaces. $ \hat D(A)$ is then characterized in two ways. $ \hat D(A)$ is the set of x such that $ S(t)x$ is locally Lipschitz continuous in t or, equivalently, the set of x which can lie in the domain of suitable extensions of A.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0313873-1
PII: S 0002-9939(1973)0313873-1
Article copyright: © Copyright 1973 American Mathematical Society