Clark measures for rational inner functions II: general bidegrees and higher dimensions

Authors

Kelly Bickel, Bucknell UniversityFollow
John Anderson, College of the Holy Cross
Linus Bergqvsist, Stockholm University
Joseph Cima, University of North Carolina at Chapel Hill
Alan Sola, Stockholm University

Publication Date

2024

Description

We study Clark measures associated with general two-variable rational inner functions (RIFs) on the bidisk, including those with singularities, and with general d-variable rational inner functions with no singularities. We give precise descriptions of support sets and weights for such Clark measures in terms of level sets and partial derivatives of the associated RIF. In two variables, we characterize when the associated Clark embeddings are unitary, and for generic parameter values, we relate vanishing of two-variable weights with the contact order of the associated RIF at a singularity.

Journal

Arkiv för Matematik

Volume

62

Issue

2

First Page

331

Last Page

368

Department

Mathematics

Recommended Citation

Bickel, Kelly; Anderson, John; Bergqvsist, Linus; Cima, Joseph; and Sola, Alan. "Clark measures for rational inner functions II: general bidegrees and higher dimensions." (2024) : 331-368.