Uniform stability of resolvent families

Lizama, Carlos; Vergara, Vicente

doi:10.1090/S0002-9939-03-07073-4

Uniform stability of resolvent families
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by Carlos Lizama and Vicente Vergara PDF

Proc. Amer. Math. Soc. 132 (2004), 175-181 Request permission

Abstract:

In this article we study uniform stability of resolvent families associated to an integral equation of convolution type. We give sufficient conditions for the uniform stability of the resolvent family in Hilbert and Banach spaces. Our main result can be viewed as a substantial generalization of the Gearhart-Greiner-Prüss characterization of exponential stability for strongly continuous semigroups.

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