Beurling–Lax type theorems in the complex and quaternionic setting

Daniel Alpay; Irene Sabadini

doi:10.1016/j.laa.2017.04.037

Beurling–Lax type theorems in the complex and quaternionic setting

Daniel Alpay, Irene Sabadini

Department of Mathematics

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

8 Scopus citations

Abstract

We give a generalization of the Beurling–Lax theorem both in the complex and quaternionic settings. We consider in the first case functions meromorphic in the right complex half-plane, and functions slice hypermeromorphic in the right quaternionic half-space in the second case. In both settings we also discuss a unified framework, which includes both the disk and the half-plane for the complex case and the open unit ball and the half-space in the quaternionic setting.

Original language	English
Pages (from-to)	15-46
Number of pages	32
Journal	Linear Algebra and Its Applications
Volume	530
DOIs	https://doi.org/10.1016/j.laa.2017.04.037
State	Published - 1 Oct 2017

Keywords

Analytic functions in the unit disk
Beurling–Lax theorem
de Branges Rovnyak spaces
in the half-plane
in the quaternionic half space
Slice hyperholomorphic functions in the quaternionic unit ball

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.2017.04.037

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abstract = "We give a generalization of the Beurling–Lax theorem both in the complex and quaternionic settings. We consider in the first case functions meromorphic in the right complex half-plane, and functions slice hypermeromorphic in the right quaternionic half-space in the second case. In both settings we also discuss a unified framework, which includes both the disk and the half-plane for the complex case and the open unit ball and the half-space in the quaternionic setting.",

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AU - Sabadini, Irene

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N2 - We give a generalization of the Beurling–Lax theorem both in the complex and quaternionic settings. We consider in the first case functions meromorphic in the right complex half-plane, and functions slice hypermeromorphic in the right quaternionic half-space in the second case. In both settings we also discuss a unified framework, which includes both the disk and the half-plane for the complex case and the open unit ball and the half-space in the quaternionic setting.

AB - We give a generalization of the Beurling–Lax theorem both in the complex and quaternionic settings. We consider in the first case functions meromorphic in the right complex half-plane, and functions slice hypermeromorphic in the right quaternionic half-space in the second case. In both settings we also discuss a unified framework, which includes both the disk and the half-plane for the complex case and the open unit ball and the half-space in the quaternionic setting.

KW - Analytic functions in the unit disk

KW - Beurling–Lax theorem

KW - de Branges Rovnyak spaces

KW - in the half-plane

KW - in the quaternionic half space

KW - Slice hyperholomorphic functions in the quaternionic unit ball

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U2 - 10.1016/j.laa.2017.04.037

DO - 10.1016/j.laa.2017.04.037

M3 - Article

AN - SCOPUS:85019085492

SN - 0024-3795

VL - 530

SP - 15

EP - 46

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Beurling–Lax type theorems in the complex and quaternionic setting

Abstract

Keywords

ASJC Scopus subject areas

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