Positive and Generalized Positive Real Lemma for Slice Hyperholomorphic Functions

Daniel Alpay; Fabrizio Colombo; Izchak Lewkowicz; Irene Sabadini

doi:10.1007/s00020-019-2503-9

Positive and Generalized Positive Real Lemma for Slice Hyperholomorphic Functions

Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini

Department of Electrical & Computer Engineering

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

2 Scopus citations

Abstract

In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic functions. We consider the case of functions with positive real part in the half space of quaternions with positive real part, as well as the case of (generalized) Schur functions in the open unit ball.

Original language	English
Article number	4
Journal	Integral Equations and Operator Theory
Volume	91
Issue number	1
DOIs	https://doi.org/10.1007/s00020-019-2503-9
State	Published - 1 Feb 2019

Keywords

Half space
Kalman–Yakubovich–Popov lemma
Negative squares
Positive real functions
Slice hyperholomorphic functions
Unit ball

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s00020-019-2503-9

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abstract = "In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic functions. We consider the case of functions with positive real part in the half space of quaternions with positive real part, as well as the case of (generalized) Schur functions in the open unit ball.",

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KW - Positive real functions

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KW - Unit ball

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Positive and Generalized Positive Real Lemma for Slice Hyperholomorphic Functions

Abstract

Keywords

ASJC Scopus subject areas

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