A proof of Bernsteinâs 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 âregularly monotonicâ 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 Bernsteinâs theorem on the analyticity of such functions.References
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S. N. BernĆĄteÇn, Leçons sur les propriĂ©tĂ©s extrĂ©males et la meilleure approximations des fonctions analytiques dâune variable rĂ©elle, Gauthier-Villar s, Paris, 1926.
- R. P. Boas Jr., Signs of derivatives and analytic behavior, Amer. Math. Monthly 78 (1971), 1085â1093. 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
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