There exist no gaps between Gevrey differentiable and nowhere Gevrey differentiable
Authors:
Soon-Yeong Chung and Jaeyoung Chung
Journal:
Proc. Amer. Math. Soc. 133 (2005), 859-863
MSC (2000):
Primary 26A27, 26A99
DOI:
https://doi.org/10.1090/S0002-9939-04-07596-3
Published electronically:
September 29, 2004
MathSciNet review:
2113937
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Abstract | References | Similar Articles | Additional Information
Abstract: We verify that there exist no gaps between Gevrey differentiable and nowhere Gevrey differentiable in the sense that for given , there is a nowhere Gevrey differentiable function on
of order
that is Gevrey differentiable of order
for any
, which also gives a strong example that is Gevrey differentiable but nowhere analytic.
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- [KK]
S. S. Kim and K.H. Kwon, Smooth (
) but nowhere analytic functions, Amer. Math. Monthly 107 (2000), 264-266.
- [R] L. Rodino, Linear Partial Differential Operators in Gevrey Spaces, World Scientific, London, 1993. MR 95c:35001
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Additional Information
Soon-Yeong Chung
Affiliation:
Department of Mathematics, Sogang University, Seoul 121–742, Korea
Email:
sychung@ccs.sogang.ac.kr
Jaeyoung Chung
Affiliation:
Department of Mathematics, Kunsan National University, Kunsan 573–701, Korea
Email:
jychung@kunsan.ac.kr
DOI:
https://doi.org/10.1090/S0002-9939-04-07596-3
Received by editor(s):
November 13, 2003
Received by editor(s) in revised form:
November 23, 2003
Published electronically:
September 29, 2004
Communicated by:
Carmen C. Chicone
Article copyright:
© Copyright 2004
American Mathematical Society