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Sibirsk. Mat. Zh., 2013, Volume 54, Number 4, Pages 725–741 (Mi smj2454)  

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

Sufficient sets in weighted Fréchet spaces of entire functions

A. V. Abaninab, V. A. Varzieva

a Southern Mathematical Institute, Vladikavkaz, Russia
b Southern Federal University, Rostov-on-Don, Russia

Abstract: Under study are sufficient sets in Fréchet spaces of entire functions with uniform weighted estimates. We obtain general results on the a priori overflow of these sets and introduce the concept of their minimality. We also establish necessary and sufficient conditions for a sequence of points on the complex plane to be a minimal sufficient set for a weighted Fréchet space. Applications are given to the problem of representation of holomorphic functions in a convex domain with certain growth near the boundary by exponential series.

Keywords: sufficient set, Fréchet space, entire function.

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English version:
Siberian Mathematical Journal, 2013, 54:4, 575–587

Bibliographic databases:

UDC: 517.983+517.5
Received: 12.10.2012

Citation: A. V. Abanin, V. A. Varziev, “Sufficient sets in weighted Fréchet spaces of entire functions”, Sibirsk. Mat. Zh., 54:4 (2013), 725–741; Siberian Math. J., 54:4 (2013), 575–587

Citation in format AMSBIB
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\by A.~V.~Abanin, V.~A.~Varziev
\paper Sufficient sets in weighted Fr\'echet spaces of entire functions
\jour Sibirsk. Mat. Zh.
\yr 2013
\vol 54
\issue 4
\pages 725--741
\mathnet{http://mi.mathnet.ru/smj2454}
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\transl
\jour Siberian Math. J.
\yr 2013
\vol 54
\issue 4
\pages 575--587
\crossref{https://doi.org/10.1134/S0037446613040010}
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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. V. A. Varziev, “Lineinyi nepreryvnyi pravyi obratnyi k operatoru predstavleniya v $(LB)$-prostranstvakh”, Vladikavk. matem. zhurn., 15:3 (2013), 37–44  mathnet
    2. J. Bonet, C. Fernandez, A. Galbis, J. M. Ribera, “Frames and representing systems in Fréchet spaces and their duals”, Banach J. Math. Anal., 11:1 (2017), 1–20  crossref  mathscinet  zmath  isi  scopus
    3. K. P. Isaev, K. V. Trounov, R. S. Yulmukhametov, “Representing systems of exponentials in projective limits of weighted subspaces of $H(D)$”, Izv. Math., 83:2 (2019), 232–250  mathnet  crossref  crossref  adsnasa  isi  elib
    4. K. P. Isaev, “Predstavlyayuschie sistemy eksponent v prostranstvakh analiticheskikh funktsii”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 3–64  mathnet  mathscinet
  • Сибирский математический журнал Siberian Mathematical Journal
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