Sets of uniqueness, weakly sufficient sets and sampling sets for weighted spaces of holomorphic functions in the unit ball. (English) Zbl 1478.32022
Summary: We consider, in a quite general setting, 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 some conditions of the weights, is obtained.
MSC:
| 32A37 | Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) |
| 46A13 | Spaces defined by inductive or projective limits (LB, LF, etc.) |
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