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Proceedings of the American Mathematical Society

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

 
 

 

One parameter groups and the characterization of the sine function


Author: Lawrence J. Wallen
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0915716-2
Article copyright: © Copyright 1988 American Mathematical Society

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