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The non-analytic growth bound of a C-0-semigroup and inhomogeneous Cauchy problems

Abstract:

The non-analytic growth bound ζ(T) of a C0-semigroup T measures the extent to which T can be approximated by a holomorphic function, and it is related to spectral properties of the generator A in regions of ℂ far from the real axis. We show that ζ(T) can be characterised by means of Fourier multiplier properties of the resolvent of A far from the real axis, and also by existence and uniqueness of mild solutions of inhomogeneous Cauchy problems of the form u′(t) = Au(t) + f(t) on ℝ where the C...

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Srivastava, S More by this author
Journal:
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume:
194
Issue:
2
Pages:
300-327
Publication date:
2003-11-01
DOI:
ISSN:
0022-0396
URN:
uuid:f79d8e9f-8eb5-4ebe-b1fe-938da286e198
Source identifiers:
12161
Local pid:
pubs:12161

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