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Sibirskii Matematicheskii Zhurnal, 2013, Volume 54, Number 4, Pages 725–741 (Mi smj2454)  
This article is cited in 5 scientific papers (total in 5 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 (5)
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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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\pages 725--741
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    • This publication is cited in the following 5 articles:
    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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