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Proceedings of the American Mathematical Society

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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Additional Information
  • R. deLaubenfels
  • Affiliation: Scientia Research Institute, P. O. Box 988, Athens, Ohio 45701
  • Email: 72260.2403@compuserve.com
  • S. Wang
  • Affiliation: Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210008, People’s Republic of China
  • Email: wang2598@netra.nju.edu.cn
  • Received by editor(s): June 12, 1996
  • Received by editor(s) in revised form: March 20, 1997
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 3271-3278
  • MSC (1991): Primary 47D03, 34G10, 47D06, 47A60
  • DOI: https://doi.org/10.1090/S0002-9939-98-04572-9
  • MathSciNet review: 1469403