RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

 Izv. Akad. Nauk SSSR Ser. Mat., 1970, Volume 34, Issue 3, Pages 584–620 (Mi izv2437)

On classification and representation of infinitely differentiable functions

Abstract: In this paper a classification of infinitely differentiable functions is developed, based on derivatives introduced earlier by the author. In terms of the classes $C_{y,x}(0,u)$ and $C_{y,x}(0,\infty)$ considered in this paper, not only is an interrelation between the different classes given, but also the problem of representation of the functions of these classes, in the case of quasi-analyticity (in the sense of Denjoy and Carleman) as well as in the case of non-quasi-analyticity of the class, is completely solved. Some applications of these results are given.

Full text: PDF file (2064 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1970, 4:3, 587–626

Bibliographic databases:

UDC: 517.5
MSC: 46E25, 40A10, 40A30

Citation: G. V. Badalyan, “On classification and representation of infinitely differentiable functions”, Izv. Akad. Nauk SSSR Ser. Mat., 34:3 (1970), 584–620; Math. USSR-Izv., 4:3 (1970), 587–626

Citation in format AMSBIB
\Bibitem{Bad70} \by G.~V.~Badalyan \paper On classification and representation of infinitely differentiable functions \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1970 \vol 34 \issue 3 \pages 584--620 \mathnet{http://mi.mathnet.ru/izv2437} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=264013} \zmath{https://zbmath.org/?q=an:0217.09103} \transl \jour Math. USSR-Izv. \yr 1970 \vol 4 \issue 3 \pages 587--626 \crossref{https://doi.org/10.1070/IM1970v004n03ABEH000923}