Interpolation without Separation in Bergman Spaces

TL;DR

This paper extends the understanding of interpolation in Bergman spaces by demonstrating that certain characterizations hold even without the uniform discreteness condition, broadening the scope of interpolation theory.

Contribution

It generalizes the concept of interpolation in Bergman spaces, removing the need for sequences to be uniformly discrete in the hyperbolic metric.

Findings

Two classical characterizations remain valid without uniform discreteness.

The generalized notion of interpolation includes simple and multiple interpolation.

Results expand the applicability of interpolation theory in Bergman spaces.

Abstract

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.