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Ufimsk. Mat. Zh., 2014, Volume 6, Issue 3, Pages 17–27 (Mi ufa250)  

This article is cited in 4 scientific papers (total in 4 papers)

On A. F. Leont'ev's interpolating function

O. A. Ivanovaa, S. N. Melikhovba

a South Federal University, Vorovich Institute of mathematics, mechanics and computer sciences, Mil'chakov str., 8a, 344090, Rostov-on-Don, Russia
b South Mathematical Institute VSC RAS, Markus str., 22, 362027, Vladikavkaz, Russia

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 $\mathrm C$ by quasipolynomial series are partial cases of the introduced interpolating functional.

Keywords: A. F. Leont'ev's interpolating function, interpolating functional, Pommiez operator.

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English version:
Ufa Mathematical Journal, 2014, 6:3, 17–27 (PDF, 343 kB); https://doi.org/10.13108/2014-6-3-17

Bibliographic databases:

UDC: 517.9
MSC: 30B50, 46A13, 47B38
Received: 22.04.2014

Citation: O. A. Ivanova, S. N. Melikhov, “On A. F. Leont'ev's interpolating function”, Ufimsk. Mat. Zh., 6:3 (2014), 17–27; Ufa Math. J., 6:3 (2014), 17–27

Citation in format AMSBIB
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\paper On A.\,F.~Leont'ev's interpolating function
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\vol 6
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet  isi  elib
    2. O. A. Ivanova, S. N. Melikhov, “Ob algebre analiticheskikh funktsionalov, svyazannoi s operatorom Pomme”, Vladikavk. matem. zhurn., 18:4 (2016), 34–40  mathnet
    3. 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  crossref  mathscinet  zmath  isi  scopus
    4. S. N. Melikhov, “Koeffitsienty ryadov eksponent dlya analiticheskikh funktsii i operator Pomme”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 65–103  mathnet
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