There exist no gaps between Gevrey differentiable and nowhere Gevrey differentiable
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- by Soon-Yeong Chung and Jaeyoung Chung PDF
- Proc. Amer. Math. Soc. 133 (2005), 859-863 Request permission
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.References
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- S. S. Kim and K.H. Kwon, Smooth ($C^{\infty }$) but nowhere analytic functions, Amer. Math. Monthly 107 (2000), 264-266.
- Luigi Rodino, Linear partial differential operators in Gevrey spaces, World Scientific Publishing Co., Inc., River Edge, NJ, 1993. MR 1249275, DOI 10.1142/9789814360036
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
- 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
- © Copyright 2004 American Mathematical Society
- 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
- MathSciNet review: 2113937