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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A faithful Hille-Yosida theorem for finite-dimensional evolutions


Author: M. A. Freedman
Journal: Trans. Amer. Math. Soc. 265 (1981), 563-573
MSC: Primary 47D05; Secondary 47D99
MathSciNet review: 610966
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Abstract: As a natural generalization of the classical Hille-Yosida theorem to evolution operators, necessary and sufficient conditions are found for an evolution $ U$ acting in $ {R^N}$ so that for each $ s \geqslant t$, $ U(s,t)$ can be uniquely represented as a product integral $ \prod _t^s{[I + V]^{ - 1}}$ for some additive, accretive generator $ V$. Under these conditions, we further show that $ U(\xi ,\zeta )$ is differentiable a.e.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0610966-5
PII: S 0002-9947(1981)0610966-5
Keywords: Evolution, generator, product and sum integral
Article copyright: © Copyright 1981 American Mathematical Society