Abstract
We generalize the theorem of Bernstein that any infinitely many times differentiable function on an interval, \(I\), that is regularly monotonic on \(I\) must be a real analytic function on \(I\).
Citation
F. S. Cater. "On Monotonic and Analytic Functions in \(C^\infty\)." Real Anal. Exchange 23 (2) 697 - 708, 1997/1998.
Information
Published: 1997/1998
First available in Project Euclid: 14 May 2012
zbMATH: 0943.26025
MathSciNet: MR1640016
Subjects:
Primary:
26A48
,
30B10
Keywords:
{analytic}
,
{change sign}
,
{power series}
,
{regularly monotonic}
,
{Taylor's Theorem}
Rights: Copyright © 1999 Michigan State University Press
