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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: September 29, 2004
MathSciNet review: 2113937
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Abstract: We verify that there exist no gaps between Gevrey differentiable and nowhere Gevrey differentiable in the sense that for given $s>1$, there is a nowhere Gevrey differentiable function on $\mathbb{R}$ of order $s$ that is Gevrey differentiable of order $r$ for any $r>s$, which also gives a strong example that is Gevrey differentiable but nowhere analytic.


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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: http://dx.doi.org/10.1090/S0002-9939-04-07596-3
PII: S 0002-9939(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