Beurling-Lax type theorems and Cuntz relations

Daniel Alpay; Fabrizio Colombo; Irene Sabadini; Baruch Schneider

doi:10.1016/j.laa.2021.10.008

Beurling-Lax type theorems and Cuntz relations

Daniel Alpay
, Fabrizio Colombo
, Irene Sabadini
, Baruch Schneider

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We prove various Beurling-Lax type theorems, when the classical backward-shift operator is replaced by a general resolvent operator associated with a rational function. We also study connections to the Cuntz relations. An important tool is a new representation result for analytic functions, in terms of composition and multiplication operators associated with a given rational function. Applications to the theory of de Branges-Rovnyak spaces, also in the indefinite metric setting, are given.

Original language	English
Pages (from-to)	152-212
Number of pages	61
Journal	Linear Algebra and Its Applications
Volume	633
DOIs	https://doi.org/10.1016/j.laa.2021.10.008
State	Published - 15 Jan 2022
Externally published	Yes

Keywords

Backward-shift operator
Beurling-Lax theorem
Cuntz relations
Rational functions
Structure theorems
de Branges-Rovnyak spaces

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2021.10.008

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title = "Beurling-Lax type theorems and Cuntz relations",

abstract = "We prove various Beurling-Lax type theorems, when the classical backward-shift operator is replaced by a general resolvent operator associated with a rational function. We also study connections to the Cuntz relations. An important tool is a new representation result for analytic functions, in terms of composition and multiplication operators associated with a given rational function. Applications to the theory of de Branges-Rovnyak spaces, also in the indefinite metric setting, are given.",

keywords = "Backward-shift operator, Beurling-Lax theorem, Cuntz relations, Rational functions, Structure theorems, de Branges-Rovnyak spaces",

author = "Daniel Alpay and Fabrizio Colombo and Irene Sabadini and Baruch Schneider",

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T1 - Beurling-Lax type theorems and Cuntz relations

AU - Alpay, Daniel

AU - Colombo, Fabrizio

AU - Sabadini, Irene

AU - Schneider, Baruch

PY - 2022/1/15

Y1 - 2022/1/15

N2 - We prove various Beurling-Lax type theorems, when the classical backward-shift operator is replaced by a general resolvent operator associated with a rational function. We also study connections to the Cuntz relations. An important tool is a new representation result for analytic functions, in terms of composition and multiplication operators associated with a given rational function. Applications to the theory of de Branges-Rovnyak spaces, also in the indefinite metric setting, are given.

AB - We prove various Beurling-Lax type theorems, when the classical backward-shift operator is replaced by a general resolvent operator associated with a rational function. We also study connections to the Cuntz relations. An important tool is a new representation result for analytic functions, in terms of composition and multiplication operators associated with a given rational function. Applications to the theory of de Branges-Rovnyak spaces, also in the indefinite metric setting, are given.

KW - Backward-shift operator

KW - Beurling-Lax theorem

KW - Cuntz relations

KW - Rational functions

KW - Structure theorems

KW - de Branges-Rovnyak spaces

UR - https://www.scopus.com/pages/publications/85117596077

U2 - 10.1016/j.laa.2021.10.008

DO - 10.1016/j.laa.2021.10.008

M3 - Article

AN - SCOPUS:85117596077

SN - 0024-3795

VL - 633

SP - 152

EP - 212

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Beurling-Lax type theorems and Cuntz relations

Abstract

Keywords

ASJC Scopus subject areas

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