Geodesic
On classification and representation of infinitely differentiable
Izvestiya. Mathematics , Tome 4 (1970) no. 3, pp. 587-626.

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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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G. V. Badalyan. On classification and representation of infinitely differentiable. Izvestiya. Mathematics , Tome 4 (1970) no. 3, pp. 587-626. http://geodesic.mathdoc.fr/item/IM2_1970_4_3_a7/

[1] Badalyan G. V., “Kriterii razlozhimosti funktsii v kvazistepennoi ryad i kvazianaliticheskie klassy funktsii”, Izv. AN SSSR. Ser. matem., 26 (1962), 839–864 | Zbl

[2] Mandelbroit S., Primykayuschie ryady. Regulyarizatsiya posledovatelnostei. Primeneniya, IL, M, 1955

[3] Badalyan G. V., “Obobschenie ryada Teilora i nekotorye voprosy teorii analiticheskikh i kvazianaliticheskikh funktsii”, Izv. AN ArmSSR, VI:5–6 (1953), 1–63 | MR

[4] Badalyan G. V., “$A_\gamma$-absolyutno monotonnye funktsii”, Izv. AN ArmSSR (ser. fiz.-matem. nauk), XIV:4 (1961), 21–35

[5] Badalyan G. V., “Nekotorye granichnye svoistva obobschennogo ryada Teilora”, Izv. AN ArmSSR (ser. fiz.-matem. nauk), XI:2 (1958), 3–29

[6] Landau E., Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie, Verlag von J. Springer, Berlin, 1916

[7] Khirshman I. I., Uidder D. V., Preobrazovanie tipa svertki, IL, M., 1958

[8] Riss F., Sekelfalvi-Nad B., Lektsii po funktsionalnomu analizu, IL, M., 1954

[9] Badalyan G. V., “Primenenie preobrazovaniya tipa svertki k teorii obobschennoi problemy momentov Stiltesa”, Izv. AN SSSR. Ser. matem., 31 (1967), 491–530 | Zbl

[10] Gelfand I. M., Shilov G. E., Prostranstva osnovnykh i obobschennykh funktsii, Obobschennye funktsii, vyp. 2, M., 1958 | Zbl

[11] Badalyan M. V., Ob odnoi teoreme edinstvennosti i ee sledstviyakh, Sbornik nauchnykh rabot ped. instituta im. X. Abovyana, Erevan, 1966