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A non-analytic growth bound for Laplace transforms and semigroups of operators

Abstract:
Let f : ℝ+ → ℂ be an exponentially bounded, measurable function. We introduce a growth bound ζ(f) which measures the extent to which f can be approximated by holomorphic functions. This growth bound is related to the location of the domain of holomorphy of the Laplace transform of f far from the real axis. The definition extends to vector and operator-valued cases. For a C0-semigroup T of operators, ζ(T) is closely related to the critical growth bound of T.
Publication status:
Published

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Publisher copy:
10.1007/s000200300000

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
INTEGRAL EQUATIONS AND OPERATOR THEORY
Volume:
45
Issue:
2
Pages:
125-154
Publication date:
2003-02-05
DOI:
ISSN:
0378-620X
URN:
uuid:5800a3bd-55d4-491c-9711-03c063b75b3e
Source identifiers:
14281
Local pid:
pubs:14281

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