Complete interpolating sequences, the discrete Muckenhoupt condition, and conformal mapping

TL;DR

This paper generalizes the parameterization of sine-type functions using conformal mappings to include generating functions of real complete interpolating sequences, revealing that the associated cuts must satisfy the discrete Muckenhoupt condition.

Contribution

It extends the conformal mapping parameterization to a broader class of generating functions for interpolating sequences, linking geometric and harmonic analysis conditions.

Findings

Cuts in the conformal mappings must satisfy the discrete Muckenhoupt condition.

Extension of sine-type function parameterization to complete interpolating sequences.

Connection between geometric domain properties and harmonic analysis conditions.

Abstract

We extend the parameterization of sine-type functions in terms of conformal mappings onto slit domains given by Eremenko and Sodin to the more general case of generating functions of real complete interpolating sequences. It turns out that the cuts have to fulfill the discrete Muckenhoupt condition studied earlier by Lyubarskii and Seip.