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.
\Bibitem{Aba15}
\by A.~V.~Abanin
\paper Sampling sets for the space of holomorphic functions of polynomial growth in a~ball
\jour Ufa Math. J.
\yr 2015
\vol 7
\issue 4
\pages 3--14
\mathnet{http://mi.mathnet.ru/eng/ufa297}
\crossref{https://doi.org/10.13108/2015-7-4-3}
\elib{https://elibrary.ru/item.asp?id=25282425}
Linking options:
https://www.mathnet.ru/eng/ufa297
https://doi.org/10.13108/2015-7-4-3
https://www.mathnet.ru/eng/ufa/v7/i4/p3
This publication is cited in the following 3 articles:
Bingyang Hu, Le Hai Khoi, “Sets of Uniqueness, Weakly Sufficient Sets and Sampling Sets for Weighted Spaces of Holomorphic Functions in the Unit Ball”, Complex Anal. Oper. Theory, 16:1 (2022)
A. V. Abanin, “Effective and sampling sets for Hörmander spaces”, Complex Anal. Oper. Theory, 12:6 (2018), 1401–1419
G. G. Braichev, V. B. Sherstyukov, “Sharp bounds for asymptotic characteristics of growth of entire functions with zeros on given sets”, J. Math. Sci., 250:3 (2020), 419–453
Citation in format AMSBIB
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