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We consider inductive limits of weighted spaces of holomorphic functions in the unit ball of $mathbb C^n$. The relationship between sets of uniqueness, weakly sufficient sets and sampling sets in these spaces is studied. In particular, the equivalence of these sets, under general conditions of the weights, is obtained.
It was known to von Neumann in the 1950s that the integer lattice $mathbb{Z}^2$ forms a uniqueness set for the Bargmann-Fock space. It was later demonstrated by Seip and Wallsten that a sequence of points $Gamma$ that is uniformly close to the intege
If $X$ is the attractor set of a conformal IFS in dimension two or three, we prove that there exists a quasiregular semigroup $G$ with Julia set equal to $X$. We also show that in dimension two, with a further assumption similar to the open set condi
Cantor sets are constructed from iteratively removing sections of intervals. This process yields a cumulative distribution function (CDF), constructed from the invariant measure associated with their iterated function systems. Under appropriate assum
It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular, Sobolev space
We discuss sampling constants for dominating sets in Bergman spaces. Our method is based on a Remez-type inequality by Andrievskii and Ruscheweyh. We also comment on extensions of the method to other spaces such as Fock and Paley-Wiener spaces.