Geodesic
Geometric meaning of the interpolation conditions in the class of functions of finite order in the half-plane
Problemy analiza, Tome 8 (2019) no. 3, pp. 96-104.

Voir la notice de l'article provenant de la source Math-Net.Ru

The aim of this paper is to study the interpolation problem in the spaces of analytical functions of finite order $\rho>1$ in the half-plane. The necessary and sufficient conditions for its solvability are found in terms of the measure defined by the nodes of interpolation.
Keywords: half-plane, function of finite order, free interpolation, Nevanlinna measure
Mots-clés : interpolation sequence. 
@article{PA_2019_8_3_a8,
     author = {K. G. Malyutin and A. L. Gusev},
     title = {Geometric meaning of the interpolation conditions in the class of functions of finite order in the half-plane},
     journal = {Problemy analiza},
     pages = {96--104},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2019_8_3_a8/}
}
TY  - JOUR
AU  - K. G. Malyutin
AU  - A. L. Gusev
TI  - Geometric meaning of the interpolation conditions in the class of functions of finite order in the half-plane
JO  - Problemy analiza
PY  - 2019
SP  - 96
EP  - 104
VL  - 8
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2019_8_3_a8/
LA  - en
ID  - PA_2019_8_3_a8
ER  - 
%0 Journal Article
%A K. G. Malyutin
%A A. L. Gusev
%T Geometric meaning of the interpolation conditions in the class of functions of finite order in the half-plane
%J Problemy analiza
%D 2019
%P 96-104
%V 8
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2019_8_3_a8/
%G en
%F PA_2019_8_3_a8
K. G. Malyutin; A. L. Gusev. Geometric meaning of the interpolation conditions in the class of functions of finite order in the half-plane. Problemy analiza, Tome 8 (2019) no. 3, pp. 96-104. http://geodesic.mathdoc.fr/item/PA_2019_8_3_a8/

[1] Carleson L., “An interpolation problem for bounded analytic functions”, Amer. J. Math., 80 (1958), 921–930 | DOI | MR | Zbl

[2] Govorov N. V., Riemann's boundary problem with infinite index, Birkhäuser, Basel–Boston–Berlin, 1994 | MR | Zbl

[3] Grishin A. F., “On regularity of the growth of subharmonic functions”, Teor. Funktsii Funktsional. Anal. i Prilozhen., 7 (1968), 59–84 (in Russian) | Zbl

[4] Levin B. Ya., Distribution of Zeros of Entire Functions, English revised edition, Amer. Math. Soc., Providence, RI, 1980 | MR

[5] Malyutin K. G., “The problem of multiple interpolation in the half-plane in the class of analytic functions of finite order and normal type”, Russian Acad. Sci. Sb. Math., 78:1 (1994), 253–266 | MR

[6] Malyutin K. G., Gusev A. L., “The interpolation problem in the spaces of analytical functions of finite order in the half-plane”, Probl. Anal. Issues Anal., 7(25), Special Issue (2018), 113–123 | DOI | MR | Zbl