Abstract:
We introduce and study an abstract version of an interpolating functional. It is defined by means of Pommiez operator acting in an countable inductive limit of weighted Fréchet spaces of entire functions and of an entire function of two complex variables. The properties of the corresponding Pommiez operator are studied. The A. F. Leont'ev's interpolating function used widely in the theory of exponentional series and convolution operators and as well as the interpolating functional applied earlier for solving the problem on the existence of a continuous linear right inverse to the operator of representation of analytic functions on a bounded convex domain in C by quasipolynomial series are partial cases of the introduced interpolating functional.
Keywords:
A. F. Leont'ev's interpolating function, interpolating functional, Pommiez operator.
\Bibitem{IvaMel14}
\by O.~A.~Ivanova, S.~N.~Melikhov
\paper On A.\,F.~Leont'ev's interpolating function
\jour Ufa Math. J.
\yr 2014
\vol 6
\issue 3
\pages 17--27
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\crossref{https://doi.org/10.13108/2014-6-3-17}
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Linking options:
https://www.mathnet.ru/eng/ufa250
https://doi.org/10.13108/2014-6-3-17
https://www.mathnet.ru/eng/ufa/v6/i3/p17
This publication is cited in the following 10 articles:
O. A. Ivanova, S. N. Melikhov, “On invertibility of Duhamel operator in spaces of ultradifferentiable functions”, Ufa Math. J., 15:4 (2023), 62–75
O. A. Ivanova, S. N. Melikhov, “Cyclic vectors and invariant subspaces of the backward shift operator in Schwartz modules”, Funct. Anal. Appl., 56:3 (2022), 188–198
O. A. Ivanova, S. N. Melikhov, “Algebry analiticheskikh funktsionalov i obobschennoe proizvedenie Dyuamelya”, Vladikavk. matem. zhurn., 22:3 (2020), 72–84
S. N. Melikhov, “Coefficients of exponential series for analytic functions and the Pommiez operator”, J. Math. Sci. (N. Y.), 257:2 (2021), 206–245
A. V. Bratishchev, “On Gelfond–Leontiev Operators of Generalized Differentiation”, J. Math. Sci. (N. Y.), 252:3 (2021), 319–344
P. A. Ivanov, S. N. Melikhov, “Pommier Operator in Spaces of Analytic Functions of Several Complex Variables”, J. Math. Sci. (N. Y.), 252:3 (2021), 345–359
O. A. Ivanova, S. N. Melikhov, “On the Completeness of Orbits of a Pommiez Operator in Weighted (LF)-Spaces of Entire Functions”, Complex Anal. Oper. Theory, 11:6 (2017), 1407–1424
O. A. Ivanova, S. N. Melikhov, “On invariant subspaces of the Pommiez operator in spaces of entire functions of exponential type”, J. Math. Sci. (N. Y.), 241:6 (2019), 760–769
O. A. Ivanova, S. N. Melikhov, “On operators which commute with the Pommiez type operator in weighted spaces of entire functions”, St. Petersburg Math. J., 28:2 (2017), 209–224
O. A. Ivanova, S. N. Melikhov, “Ob algebre analiticheskikh funktsionalov, svyazannoi s operatorom Pomme”, Vladikavk. matem. zhurn., 18:4 (2016), 34–40
Citation in format AMSBIB
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