Spectral conditions guaranteeing a nontrivial solution of the abstract Cauchy problem

deLaubenfels, R.; Wang, S.

doi:10.1090/S0002-9939-98-04572-9

Spectral conditions guaranteeing a nontrivial solution of the abstract Cauchy problem
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by R. deLaubenfels and S. Wang PDF

Proc. Amer. Math. Soc. 126 (1998), 3271-3278 Request permission

Abstract:

We characterize subsets, $\Omega$, of the complex plane, with the following property: If $A$ has spectrum contained in $\Omega$, with polynomially bounded resolvent outside $\Omega$, then the abstract Cauchy problem corresponding to $A$ has a nontrivial solution.

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