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The behavior of the analytically continued resolvent operator near $ \kappa=0$ and an application to energy decay

Author: Kazuhiro Yamamoto
Journal: Proc. Amer. Math. Soc. 115 (1992), 985-993
MSC: Primary 35P05; Secondary 35L05, 47F05
MathSciNet review: 1089414
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Abstract: We shall study the behavior of the analytically continued resolvent operator $ {R^ + }(\kappa )$ for perturbations of $ - \Delta $ in a neighborhood of $ \kappa = 0$. As an application, making use of Vainberg's argument, we shall show the local energy decay of solutions to generalized wave equations whose stationary problems are not positive definite.

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Keywords: Exterior problem, resolvent operator, energy decay
Article copyright: © Copyright 1992 American Mathematical Society

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