Abstract:
The aim of this paper is to study the interpolation problem in the spaces of analytical functions of finite order ρ>1 in the half-plane. The necessary and sufficient conditions for its solvability in terms of the canonical Nevanlinna product of nodes of interpolation are obtained. The solution of the interpolation problem is constructed in the form of the Jones interpolation series, which is a generalization of the Lagrange interpolation series.
Keywords:
half-plane, function of finite order, free interpolation, Nevanlinna product, interpolation series.
Citation:
K. G. Malyutin, A. L. Gusev, “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
\Bibitem{MalGus18}
\by K.~G.~Malyutin, A.~L.~Gusev
\paper The interpolation problem in the spaces of analytical functions of finite order in the half-plane
\jour Probl. Anal. Issues Anal.
\yr 2018
\vol 7(25)
\pages 113--123
\issueinfo special issue
\mathnet{http://mi.mathnet.ru/pa236}
\crossref{https://doi.org/10.15393/j3.art.2018.5170}
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\elib{https://elibrary.ru/item.asp?id=35688767}
Linking options:
https://www.mathnet.ru/eng/pa236
https://www.mathnet.ru/eng/pa/v25/i3/p113
This publication is cited in the following 4 articles:
K. G. Malyutin, A. A. Naumova, “Predstavlenie subgarmonicheskikh funktsii v polukoltse i v polukruge”, Chebyshevskii sb., 24:5 (2023), 136–152
K. Malyutin, M. Kabanko, I. Kozlova, “Multiple Interpolation by the Functions of Finite Order in the Half-plane. II”, Lobachevskii J Math, 42:4 (2021), 811
K. Malyutin, M. Kabanko, “Multiple Interpolation by the Functions of Finite Order in the Half-Plane”, Lobachevskii J Math, 41:11 (2020), 2211
K. G. Malyutin, A. L. Gusev, “Geometric meaning of the interpolation conditions in the class of functions of finite order in the half-plane”, Probl. anal. Issues Anal., 8(26):3 (2019), 96–104
Citation in format AMSBIB
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