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

An operator-theoretic formulation of asynchronous exponential growth

Author: G. F. Webb
Journal: Trans. Amer. Math. Soc. 303 (1987), 751-763
MSC: Primary 47D05; Secondary 47B55, 92A15
MathSciNet review: 902796
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Abstract: A strongly continuous semigroup of bounded linear operators $ T(t)$, $ t \geqslant 0$, in the Banach space $ X$ has asynchronous exponential growth with intrinsic growth constant $ {\lambda _0}$ provided that there is a nonzero finite rank operator $ {P_0}$ in $ X$ such that $ {\lim _{t \to \infty }}{e^{ - {\lambda _0}t}}T(t) = {P_0}$. Necessary and sufficient conditions are established for $ T(t)$, $ t \geqslant 0$, to have asynchronous exponential growth. Applications are made to a maturity-time model of cell population growth and a transition probability model of cell population growth.

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PII: S 0002-9947(1987)0902796-7
Article copyright: © Copyright 1987 American Mathematical Society