Prevalence of  ''nowhere analyticity''

[en] This note brings a complement to the study of genericity of functions which are nowhere analytic mainly in a measure-theoretic sense. We extend this study in Gevrey classes of functions.

Disciplines :

Mathematics

Author, co-author :

Bastin, Françoise ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Esser, Céline ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Nicolay, Samuel ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Language :

English

Title :

Prevalence of ''nowhere analyticity''

Publication date :

2012

Journal title :

Studia Mathematica

ISSN :

0039-3223

eISSN :

1730-6337

Publisher :

Polish Academy of Science, Warszawa, Poland

Volume :

210

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 22 August 2012

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Bibliography

[B1] L. Bernal-Gonz-Alez, Lineability of sets of nowhere analytic functions, J. Math. Anal. Appl. 340 (2008), 1284-1295.
[B2] L. Bernal-Gonz-Alez, Funciones con derivadas sucesivas grandes y peque~nas por doquier, Collect. Math. 38 (1987), 117-122.
[B3] R. P. Boas, A theorem on analytic functions of a real variable, Bull. Amer. Math. Soc. 41 (1935), 233-236.
[B4] R. P. Boas, When is a C1 function analytic?, Math. Intelligencer 11 (1989), 40.
[C] F.S. Cater, Di-erentiable, nowhere analytic functions, Amer. Math. Monthly 91 (1984), 618-624.
[CC] S .Y. Chung and J. Chung, There exist no gaps between Gevrey di-erentiable and nowhere Gevrey di-erentiable, Proc. Amer. Math. Soc. 133 (2005), 859-863. (Pubitemid 40322777)
[HSY] B. R. Hunt, T. Sauer and J. A. Yorke, Prevalence: a translation-invariant \almost every" on in-nite-dimensional spaces, Bull. Amer. Math. Soc. 27 (1992), 217-238.
[R1] T. I. Ramsamujh, Nowhere analytic C1 functions, J. Math. Anal. Appl. 160 (1991), 263-266.
[R2] L. Rodino, Linear Partial Di-erential Operators in Gevrey Spaces, Word Sci., London, 1993.
[R3] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966.
[SZ] H. Salzmann und K. Zeller, Singularit̀aten unendlich oft di-erenzierbarer Funktionen, Math. Z. 62 (1955), 354-367.
[S] H. Shi, Prevalence of some known typical properties, Acta Math. Univ. Comeniane 70 (2001), 2, 185-192.

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