An operator-theoretic formulation of asynchronous exponential growth
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- by G. F. Webb PDF
- Trans. Amer. Math. Soc. 303 (1987), 751-763 Request permission
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.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- 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