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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The behavior of the analytically continued resolvent operator near $\kappa =0$ and an application to energy decay
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by Kazuhiro Yamamoto
Proc. Amer. Math. Soc. 115 (1992), 985-993
DOI: https://doi.org/10.1090/S0002-9939-1992-1089414-2
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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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Bibliographic Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 115 (1992), 985-993
  • MSC: Primary 35P05; Secondary 35L05, 47F05
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1089414-2
  • MathSciNet review: 1089414