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Ufimsk. Mat. Zh., 2015, Volume 7, Issue 4, Pages 3–14 (Mi ufa297)  

This article is cited in 2 scientific papers (total in 2 papers)

Sampling sets for the space of holomorphic functions of polynomial growth in a ball

A. V. Abaninab

a Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia
b Southern Federal University, Rostov-on-Don, Russia

Abstract: We develop a new approach to study sampling sets in the space of holomorphic functions of polynomial growth in a ball in the sense of Horowitz, Korenblum, and Pinchuk (Michigan Math. J., 44:2, 1997). It is based on involving weakly sufficient sets for intermediate inductive limits. By means of this approach we obtain a complete topological description of such sets and, as an application of this description, some new properties of sampling sets of general and special type are established. In particular, the main result of the above mentioned paper on sampling sequences of circles is extended to the multi-dimensional case.

Keywords: sampling sets, weakly sufficient sets, space of holomorphic functions of polynomial growth.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-0140415 a


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English version:
Ufa Mathematical Journal, 2015, 7:4, 3–14 (PDF, 203 kB); https://doi.org/10.13108/2015-7-4-3

UDC: 517.9+517.5
MSC: 32A38, 32C18, 46A13
Received: 22.07.2015

Citation: A. V. Abanin, “Sampling sets for the space of holomorphic functions of polynomial growth in a ball”, Ufimsk. Mat. Zh., 7:4 (2015), 3–14; Ufa Math. J., 7:4 (2015), 3–14

Citation in format AMSBIB
\Bibitem{Aba15}
\by A.~V.~Abanin
\paper Sampling sets for the space of holomorphic functions of polynomial growth in a~ball
\jour Ufimsk. Mat. Zh.
\yr 2015
\vol 7
\issue 4
\pages 3--14
\mathnet{http://mi.mathnet.ru/ufa297}
\elib{https://elibrary.ru/item.asp?id=25282425}
\transl
\jour Ufa Math. J.
\yr 2015
\vol 7
\issue 4
\pages 3--14
\crossref{https://doi.org/10.13108/2015-7-4-3}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. G. Braichev, V. B. Sherstyukov, “Tochnye otsenki asimptoticheskikh kharakteristik rosta tselykh funktsii s nulyami na zadannykh mnozhestvakh”, Fundament. i prikl. matem., 22:1 (2018), 51–97  mathnet
    2. A. V. Abanin, “Effective and sampling sets for Hörmander spaces”, Complex Anal. Oper. Theory, 12:6 (2018), 1401–1419  crossref  mathscinet  zmath  isi  scopus
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