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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A proof of Bernstein’s theorem on regularly monotonic functions
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by J. A. M. McHugh PDF
Proc. Amer. Math. Soc. 47 (1975), 358-360 Request permission

Abstract:

A function is called “regularly monotonic” if it is of class ${C^\infty }$ and each derivative is of a fixed sign (which may depend on the order of the derivative). We present a short proof of Bernstein’s theorem on the analyticity of such functions.
References
    S. N. BernĆĄteǐn, Leçons sur les propriĂ©tĂ©s extrĂ©males et la meilleure approximations des fonctions analytiques d’une variable rĂ©elle, Gauthier-Villar s, Paris, 1926.
  • R. P. Boas Jr., Signs of derivatives and analytic behavior, Amer. Math. Monthly 78 (1971), 1085–1093. MR 296236, DOI 10.2307/2316310
  • Ralph P. Boas Jr., A primer of real functions, The Carus Mathematical Monographs, No. 13, Mathematical Association of America; distributed by John Wiley and Sons, Inc.; New York, 1960. MR 0118779
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 47 (1975), 358-360
  • MSC: Primary 26A90
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0354974-3
  • MathSciNet review: 0354974