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Sibirskii Matematicheskii Zhurnal, 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
Full-text PDF (386 kB) Citations (4)
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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.
Received: 12.10.2012
English version:
Siberian Mathematical Journal, 2013, Volume 54, Issue 4, Pages 575–587
DOI: https://doi.org/10.1134/S0037446613040010
Bibliographic databases:
Document Type: Article
UDC: 517.983+517.5
Language: Russian
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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Linking options:
  • https://www.mathnet.ru/eng/smj2454
  • https://www.mathnet.ru/eng/smj/v54/i4/p725
    • This publication is cited in the following 4 articles:
    1. 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  mathscinet  zmath  adsnasa  isi  elib
    2. K. P. Isaev, “Representing exponential systems in spaces of analytical functions”, J. Math. Sci. (N. Y.), 257:2 (2021), 143–205  mathnet  crossref  mathscinet
    3. 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
    4. V. A. Varziev, “Lineinyi nepreryvnyi pravyi obratnyi k operatoru predstavleniya v $(LB)$-prostranstvakh”, Vladikavk. matem. zhurn., 15:3 (2013), 37–44  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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