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

DOI:
https://doi.org/10.1090/S0002-9947-1987-0902796-7

MathSciNet review:
902796

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Abstract: A strongly continuous semigroup of bounded linear operators , , in the Banach space has asynchronous exponential growth with intrinsic growth constant provided that there is a nonzero finite rank operator in such that . Necessary and sufficient conditions are established for , , 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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DOI:
https://doi.org/10.1090/S0002-9947-1987-0902796-7

Article copyright:
© Copyright 1987
American Mathematical Society