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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 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


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:
  • S. Wang
  • Affiliation: Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210008, People’s Republic of China
  • Email:
  • 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:
  • MathSciNet review: 1469403