Clark Measures for Rational Inner Functions

Publication Date

11-2023

Description

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)" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 16.8px; overflow-wrap: normal; text-wrap: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; font-family: "Open Sans", sans-serif; position: relative;">(n,1)(�,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.

Journal

Michigan Math. J.

Volume

73

Issue

5

First Page

1021

Last Page

1057

Department

Mathematics

DOI

https://doi.org/10.1307/mmj/20216046

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