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

On classification and representation of infinitely differentiable functions

G. V. Badalyan


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.

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

Bibliographic databases:

UDC: 517.5
MSC: 46E25, 40A10, 40A30
Received: 29.08.1968

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}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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