Clark Measures for Rational Inner Functions
Functional Analysis
2023-12-12 v1 Complex Variables
Abstract
We analyze the fine structure of Clark measures and Clark isometries associated with two-variable rational inner functions on the bidisk. In the degree (n,1) case, we give a complete description of supports and weights for both generic and exceptional Clark measures, characterize when the associated embedding operators are unitary, and give a formula for those embedding operators. We also highlight connections between our results and both the structure of Agler decompositions and study of extreme points for the set of positive pluriharmonic measures on 2-torus.
Cite
@article{arxiv.2101.00508,
title = {Clark Measures for Rational Inner Functions},
author = {Kelly Bickel and Joseph A. Cima and Alan A. Sola},
journal= {arXiv preprint arXiv:2101.00508},
year = {2023}
}
Comments
32 pages