Geodesic
On the disc of meromorphy of a regular $C$-fraction
Sbornik. Mathematics, Tome 206 (2015) no. 2, pp. 201-210 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider families of regular continued $C$-fractions with parameters determined by the values of a function on the orbit of a point in the phase space of a dynamical system. We prove that the radius of meromorphy of such a fraction is constant almost everywhere. Bounds for this constant are found. Bibliography: 10 titles.
Keywords: power series, regular $C$-fraction, disc of meromorphy, stationary random process. 
@article{SM_2015_206_2_a1,
     author = {V. S. Buyarov},
     title = {On the disc of meromorphy of a~regular $C$-fraction},
     journal = {Sbornik. Mathematics},
     pages = {201--210},
     year = {2015},
     volume = {206},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2015_206_2_a1/}
}
TY  - JOUR
AU  - V. S. Buyarov
TI  - On the disc of meromorphy of a regular $C$-fraction
JO  - Sbornik. Mathematics
PY  - 2015
SP  - 201
EP  - 210
VL  - 206
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_2015_206_2_a1/
LA  - en
ID  - SM_2015_206_2_a1
ER  - 
%0 Journal Article
%A V. S. Buyarov
%T On the disc of meromorphy of a regular $C$-fraction
%J Sbornik. Mathematics
%D 2015
%P 201-210
%V 206
%N 2
%U http://geodesic.mathdoc.fr/item/SM_2015_206_2_a1/
%G en
%F SM_2015_206_2_a1
V. S. Buyarov. On the disc of meromorphy of a regular $C$-fraction. Sbornik. Mathematics, Tome 206 (2015) no. 2, pp. 201-210. http://geodesic.mathdoc.fr/item/SM_2015_206_2_a1/

[1] W. B. Jones, W. J. Thron, Continued fractions. Analytic theory and applications, Encyclopedia Math. Appl., 11, Addison-Wesley Publishing Co., Reading, Mass., 1980, xxix+428 pp. | MR | MR | Zbl

[2] T. I. Stiltes, Issledovaniya o nepreryvnykh drobyakh, ONTI, Kharkov–Kiev, 1936, 160 pp.; T.-J. Stieltjes, “Recherches sur les fractions continues”, Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys., 8:4 (1894), J1–J122 ; Suite et fin, 9:1 (1895), A5–A47 | MR | Zbl | MR

[3] L. J. Rogers, “On the representation of certain asymptotic series as convergent continued fractions”, Proc. London Math. Soc., 2–4:1 (1907), 72–89 | DOI | MR | Zbl

[4] N. P. Callas, W. J. Thron, “Singularities of meromorphic functions represented by regular $C$-fractions”, Norske Vid. Selsk. Skr. (Trondheim), 1967, no. 6, 11 pp | MR | Zbl

[5] N. P. Callas, W. J. Thron, “Singular points of certain functions represented by $C$-fractions”, J. Indian Math. Soc. (N.S.), 32, suppl. I (1968), 325–353 | MR | Zbl

[6] N. P. Callas, W. J. Thron, “Singularities of a class of meromorphic functions”, Proc. Amer. Math. Soc., 33:2 (1972), 445–454 | DOI | MR | Zbl

[7] J. Worpitsky, “Untersuchungen über die Entwickelung der monodromen und monogenen Funktionen durch Kettenbruche”, Friedrichs-Gymnasium und Realschule Jahresbericht, Berlin, 1865, 3–39

[8] V. I. Buslaev, “Convergence of the Rogers–Ramanujan continued fraction”, Sb. Math., 194:6 (2003), 833–856 | DOI | DOI | MR | Zbl

[9] G. M. Goluzin, Geometric theory of functions of a complex variable, Transl. Math. Monogr., 26, Amer. Math. Soc., Providence, R.I., 1969, vi+676 pp. | MR | MR | Zbl | Zbl

[10] G. Polya, “Beitrag zur Verallgemeinerung des Verzerrungssatzes auf mehrfach zusammenhängende Gebiete. III”, Sitzungsber. Preuss. Akad. Wiss. Phys.-Math. Kl., 1929, 55–62 | Zbl