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Most characterizations of interpolating sequences for Bergman spaces include the condition that the sequence be uniformly discrete in the hyperbolic metric. We show that if the notion of interpolation is suitably generalized, two of these characterizations remain valid without that condition. The general interpolation we consider here includes the usual simple interpolation and multiple interpolation as special cases.
We extend our work on nonseparated interpolating sequences, originally developed for Bergman spaces with weights of the form $(1 - |z|^2)^alpha$, to more general weights.
In this paper we consider interpolation in model spaces, $H^2 ominus B H^2$ with $B$ a Blaschke product. We study unions of interpolating sequences for two sequences that are far from each other in the pseudohyperbolic metric as well as two sequences
Expected duality and approximation properties are shown to fail on Bergman spaces of domains in $mathbb{C}^n$, via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation results are prov
We give a proof that every space of weighted square-integrable holomorphic functions admits an equivalent weight whose Bergman kernel has zeroes. Here the weights are equivalent in the sense that they determine the same space of holomorphic functions
In this paper we study the compactness of operators on the Bergman space of the unit ball and on very generally weighted Bargmann-Fock spaces in terms of the behavior of their Berezin transforms and the norms of the operators acting on reproducing ke