Article
Ufa Mathematical Journal
Volume 7, Number 4, pp. 3-14
Sampling sets for the space of holomorphic functions of polynomial growth in a ball
Abanin A.V.
DOI:10.13108/2015-7-4-3
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We develop a new approach to study sampling sets in the sense of Horowitz, Korenblum, and Pinchuk (Michigan Math. J., 44:2, 1997) in the space of holomorphic functions of polynomial growth in a ball. 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.