Geodesic
On Stolz's theorem and its conversion
Eurasian mathematical journal, Tome 10 (2019) no. 3, pp. 8-19 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The present paper extends and refines some results on the relative growth rate of real sequences. Various forms of Stolz's theorem and its conversion are considered. 
@article{EMJ_2019_10_3_a0,
     author = {G. G. Braichev},
     title = {On {Stolz's} theorem and its conversion},
     journal = {Eurasian mathematical journal},
     pages = {8--19},
     year = {2019},
     volume = {10},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2019_10_3_a0/}
}
TY  - JOUR
AU  - G. G. Braichev
TI  - On Stolz's theorem and its conversion
JO  - Eurasian mathematical journal
PY  - 2019
SP  - 8
EP  - 19
VL  - 10
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/EMJ_2019_10_3_a0/
LA  - en
ID  - EMJ_2019_10_3_a0
ER  - 
%0 Journal Article
%A G. G. Braichev
%T On Stolz's theorem and its conversion
%J Eurasian mathematical journal
%D 2019
%P 8-19
%V 10
%N 3
%U http://geodesic.mathdoc.fr/item/EMJ_2019_10_3_a0/
%G en
%F EMJ_2019_10_3_a0
G. G. Braichev. On Stolz's theorem and its conversion. Eurasian mathematical journal, Tome 10 (2019) no. 3, pp. 8-19. http://geodesic.mathdoc.fr/item/EMJ_2019_10_3_a0/

[1] A. V. Abanin, Ultradifferentiable functions and ultradistributions, Nauka, M., 2007 (in Russian) | MR

[2] A. V. Abanin, V. V. Yudelevich, “On the conversion of Stolz's theorem”, Izv. VUZov. Sev. Kavk. Region. Est. Nauki, 2016, no. 2, 5–9 (in Russian) | MR

[3] M. Biernacki, J. Krzyz, “On the monotonicity of certain functionals in the theory of analytic functions”, Ann. Univ. M. Curie-Sklodowska, 2 (1995), 134–145 | MR

[4] G. G. Braichev, “Exact relationships between certain characteristics of growth for complex sequences”, Ufimsk. Mat. Zh., 5:4 (2013), 17–30 | MR

[5] G. G. Braichev, Introduction to the theory of growth of convex and entire functions, Prometei, M., 2005 (in Russian)

[6] H. Komatsu, “Ultradistributions I. Structure theorems and a charactersation”, J. Fac. Sci. Univ. Tokyo. Sec IA, Math., 20:1 (1973), 25–105 | MR | Zbl

[7] S. Mandelbrojt, Series adherentes, regularisation des suites, applications, Gauthier-Villars, Paris, 1952 | MR | Zbl

[8] C. Roumieu, “Sur quelques extansion de la notion de distribution”, Ann. Sci. Ecole Norm. Sup. III Ser., 77:1 (1960), 41–121 | MR | Zbl

[9] S. M. Shah, “Trigonometric series with quasi-monotone coefficients”, Proc. Amer. Math. Soc., 13 (1962), 266–273 | MR | Zbl

[10] O. Stolz, Vorlesungen über allgemeine Arithmetik: nach den Neuen Ansichten, Teubners, Leipzig, 1885, 173–175