# Sets of uniqueness, weakly sufficient sets and sampling sets for weighted spaces of holomorphic functions in the unit ball

## TL;DR

This paper investigates the relationships between various special sets in weighted spaces of holomorphic functions in the unit ball, establishing conditions under which these sets are equivalent.

## Contribution

It provides new results on the equivalence of sets of uniqueness, weakly sufficient sets, and sampling sets in inductive limits of weighted holomorphic function spaces.

## Key findings

- Equivalence of sets under general weight conditions
- Characterization of sampling sets in these spaces
- Insights into the structure of weighted holomorphic function spaces

## Abstract

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.