Abstract:
In the paper we consider the problem of multiple interpolation in a class of functions of a zero order and type not exceeding normal in the upper halfplane of the complex variable. This problem belongs to the class of problems of free interpolation considered initially by A. F. Leont'ev. We find necessary and sufficient solvability conditions for this problem. The found criteria are formulated in terms of the canonical products constructed on knots of interpolation, and in terms of the Nevanlinna measure determined by these knots. The work is a continuation of researches of the first author considered similar problems in classes of analytic functions in the upper half-plane of a nonzero order.
Citation:
O. A. Bozhenko, K. G. Malyutin, “Problem of multiple interpolation in class of analytical functions of zero order in half-plane”, Ufa Math. J., 6:1 (2014), 18–28
\Bibitem{BozMal14}
\by O.~A.~Bozhenko, K.~G.~Malyutin
\paper Problem of multiple interpolation in class of analytical functions of zero order in half-plane
\jour Ufa Math. J.
\yr 2014
\vol 6
\issue 1
\pages 18--28
\mathnet{http://mi.mathnet.ru/eng/ufa230}
\crossref{https://doi.org/10.13108/2014-6-1-18}
\elib{https://elibrary.ru/item.asp?id=21290424}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928201077}
Linking options:
https://www.mathnet.ru/eng/ufa230
https://doi.org/10.13108/2014-6-1-18
https://www.mathnet.ru/eng/ufa/v6/i1/p18
This publication is cited in the following 3 articles:
M. V. Kabanko, K. G. Malyutin, “Interpolation sets in spaces of functions of finite order in half–plane”, Ufa Math. J., 16:3 (2024), 40–53
Malyutin K.G., Kabanko V M., Applied Mathematics, Computational Science and Mechanics: Current Problems, Journal of Physics Conference Series, 1479, IOP Publishing Ltd, 2020
K. G. Malyutin, “Interpolation Problems of A. F. Leontiev Type”, J. Math. Sci. (N. Y.), 252:3 (2021), 399–419