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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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One parameter groups and the characterization of the sine function
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by Lawrence J. Wallen PDF
Proc. Amer. Math. Soc. 102 (1988), 59-60 Request permission

Abstract:

A real ${C^\infty }$ function on ${{\mathbf {R}}^1}$, all of whose derivatives and (suitable) antiderivatives are uniformly bounded, is of the form $a\sin (x - {x_0})$. We give an abstract version of this theorem.
References
  • J. Roe, A characterization of the sine function, Math. Proc. Cambridge Philos. Soc. 87 (1980), no. 1, 69–73. MR 549299, DOI 10.1017/S030500410005653X
    • J. A. van Casteren, Generators of strongly continuous semigroups, Pitman, Boston, Mass., 1985.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 102 (1988), 59-60
  • MSC: Primary 47D10,; Secondary 47B25
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0915716-2
  • MathSciNet review: 915716