Herglotz functions: The Fueter variables case

Daniel Alpay; Fabrizio Colombo; Irene Sabadini

doi:10.1016/j.laa.2018.10.013

Herglotz functions: The Fueter variables case

Daniel Alpay, Fabrizio Colombo, Irene Sabadini

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

Abstract

In this paper we provide realizations of Herglotz functions in the quaternionic case where hyperholomorphic functions are meant in the sense of Fueter. We consider the counterparts of the Arveson space and of the Herglotz–Agler functions by introducing suitable positive kernels. Crucial tools are the so-called Fueter variables and the CK-product. Our realization results also show that positivity implies analyticity.

Original language	English
Pages (from-to)	75-97
Number of pages	23
Journal	Linear Algebra and Its Applications
Volume	563
DOIs	https://doi.org/10.1016/j.laa.2018.10.013
State	Published - 15 Feb 2019
Externally published	Yes

Keywords

Arveson space
Fueter variables
Herglotz functions

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.2018.10.013

Cite this

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title = "Herglotz functions: The Fueter variables case",

abstract = "In this paper we provide realizations of Herglotz functions in the quaternionic case where hyperholomorphic functions are meant in the sense of Fueter. We consider the counterparts of the Arveson space and of the Herglotz–Agler functions by introducing suitable positive kernels. Crucial tools are the so-called Fueter variables and the CK-product. Our realization results also show that positivity implies analyticity.",

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T2 - The Fueter variables case

AU - Alpay, Daniel

AU - Colombo, Fabrizio

AU - Sabadini, Irene

PY - 2019/2/15

Y1 - 2019/2/15

N2 - In this paper we provide realizations of Herglotz functions in the quaternionic case where hyperholomorphic functions are meant in the sense of Fueter. We consider the counterparts of the Arveson space and of the Herglotz–Agler functions by introducing suitable positive kernels. Crucial tools are the so-called Fueter variables and the CK-product. Our realization results also show that positivity implies analyticity.

AB - In this paper we provide realizations of Herglotz functions in the quaternionic case where hyperholomorphic functions are meant in the sense of Fueter. We consider the counterparts of the Arveson space and of the Herglotz–Agler functions by introducing suitable positive kernels. Crucial tools are the so-called Fueter variables and the CK-product. Our realization results also show that positivity implies analyticity.

KW - Arveson space

KW - Fueter variables

KW - Herglotz functions

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U2 - 10.1016/j.laa.2018.10.013

DO - 10.1016/j.laa.2018.10.013

M3 - Article

AN - SCOPUS:85055668354

SN - 0024-3795

VL - 563

SP - 75

EP - 97

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Herglotz functions: The Fueter variables case

Abstract

Keywords

ASJC Scopus subject areas

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