On Uniformly Discrete Sequences in the Disk

We present an overview of uniformly discrete sequences and their relationship to other important types of sets, such as uniformly separated sequences, sets of interpolation and sampling, and zero-sets for Bergman spaces. Introduction A sequence Γ = {zk} in the unit disk D is said to be uniformly discrete if ρ(zj , zk) = ∣∣∣∣ zj − zk 1− zjzk ∣∣∣∣ ≥ δ for some fixed δ > 0 and all j 6= k. The supremum of all such δ is called the separation constant of Γ and is denoted by δ(Γ). For 0 < p <∞ the Bergman space A consists of those functions f analytic in D for which the area integral ‖f‖p = ∫