Geodesic
On uniqueness of holomorphic and bounded outside the closed logarithmic sector functions representable by lacunary power series
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2009), pp. 61-63 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the present note it is shown that for a set of positive integers $\Lambda$ a Müntz- type condition holds if and only if there exists a lacunary power series $f(z)=\displaystyle\sum_{v\in\Lambda}f_v/z^v$ that allows an analytic and bounded continuation to the complement of a closed logarithmical sector with vertex at the origin.
Keywords: closed logarithmic sector, lacunary power series, coefficient function method, analytic continuation. 
@article{UZERU_2009_1_a11,
     author = {S. E. Mkrtchyan},
     title = {On uniqueness of holomorphic and bounded outside the closed logarithmic sector functions representable by lacunary power series},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {61--63},
     year = {2009},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2009_1_a11/}
}
TY  - JOUR
AU  - S. E. Mkrtchyan
TI  - On uniqueness of holomorphic and bounded outside the closed logarithmic sector functions representable by lacunary power series
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2009
SP  - 61
EP  - 63
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UZERU_2009_1_a11/
LA  - en
ID  - UZERU_2009_1_a11
ER  - 
%0 Journal Article
%A S. E. Mkrtchyan
%T On uniqueness of holomorphic and bounded outside the closed logarithmic sector functions representable by lacunary power series
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2009
%P 61-63
%N 1
%U http://geodesic.mathdoc.fr/item/UZERU_2009_1_a11/
%G en
%F UZERU_2009_1_a11
S. E. Mkrtchyan. On uniqueness of holomorphic and bounded outside the closed logarithmic sector functions representable by lacunary power series. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2009), pp. 61-63. http://geodesic.mathdoc.fr/item/UZERU_2009_1_a11/

[1] L. Freric, V.A. Martirosian, J. Müller, “On the existence of lacunary power series analytically continuable and bounded outside sectors”, Comp. var. elliptic equation, 54:7 (2009), 669–676 | DOI | MR | Zbl

[2] Math. USSR-Sb., 52:1 (1985), 21–39 | DOI | MR | Zbl

[3] L. Bieberbach, Analytische Fortsetzung, Spriger, Berlin, 1955 | MR | Zbl

[4] V.A. Martirosian, “On entire functions bounded on a closed angle and representable by power series with gaps or real coefficients”, Dokl. Akad. Nauk SSSR, 1986, no. 6, 1301–1304 (in Russian) | MR

[5] R.P. Boas, Entire functions, Academic Press, New York, 1954 | MR | Zbl

[6] W.H.J. Fuchs, “A Generalization of Carlson's Theorem”, J.London Math. Soc., 1946, 106–110 | DOI | MR | Zbl