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
Slice hyperholomorphic functions in the quaternionic unit ball
de Branges Rovnyak spaces
in the half-plane
in the quaternionic half space

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 - Alpay, Daniel

AU - Sabadini, Irene

PY - 2017/10/1

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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 - Slice hyperholomorphic functions in the quaternionic unit ball

KW - de Branges Rovnyak spaces

KW - in the half-plane

KW - in the quaternionic half space

UR - https://www.scopus.com/pages/publications/85019085492

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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