Analyticity and quasi-analyticity for one-parameter semigroups

Author:
J. W. Neuberger

Journal:
Proc. Amer. Math. Soc. **25** (1970), 488-494

MSC:
Primary 47.50

DOI:
https://doi.org/10.1090/S0002-9939-1970-0259661-3

MathSciNet review:
0259661

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Abstract: Suppose that is a strongly continuous (even at 0) one-parameter semigroup of bounded linear transformations on a real Banach space and has generator . Theorem A. *If* *then* *is bounded for all* . Suppose is a sequence of positive numbers convergent to 0 and each of is an increasing sequence of positive integers. Denote by the collection consisting of (1) all real analytic functions on and (2) all on for which there is a Banach space , a member of , a member of and a strongly continuous semigroup of bounded linear transformations so that for all where satisfies . Theorem B. *No two members of* *agree on an open subset of* .

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DOI:
https://doi.org/10.1090/S0002-9939-1970-0259661-3

Keywords:
Quasi-analytic,
analytic,
semigroup of bounded linear transformations

Article copyright:
© Copyright 1970
American Mathematical Society