Herglotz functions of several quaternionic variables

Khaled Abu-Ghanem; Daniel Alpay; Fabrizio Colombo; Izchak Lewkowicz; Irene Sabadini

doi:10.1016/j.jmaa.2018.05.066

Herglotz functions of several quaternionic variables

Khaled Abu-Ghanem, Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini

Department of Electrical & Computer Engineering

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

5 Scopus citations

Abstract

We first review realizations of Herglotz functions in the unit ball of C^N and provide new insights. Then, we define the corresponding class and prove the extend the results in the case of several quaternionic variables.

Original language	English
Pages (from-to)	169-182
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	466
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2018.05.066
State	Published - 1 Oct 2018

Keywords

Gleason's problem
Herglotz functions
Several complex variables
Several quaternionic variables

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2018.05.066

Cite this

@article{a47fd78a6b7741a2b2a4aafc539e613a,

title = "Herglotz functions of several quaternionic variables",

abstract = "We first review realizations of Herglotz functions in the unit ball of CN and provide new insights. Then, we define the corresponding class and prove the extend the results in the case of several quaternionic variables.",

keywords = "Gleason's problem, Herglotz functions, Several complex variables, Several quaternionic variables",

author = "Khaled Abu-Ghanem and Daniel Alpay and Fabrizio Colombo and Izchak Lewkowicz and Irene Sabadini",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

month = oct,

day = "1",

doi = "10.1016/j.jmaa.2018.05.066",

language = "English",

volume = "466",

pages = "169--182",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Herglotz functions of several quaternionic variables

AU - Abu-Ghanem, Khaled

AU - Alpay, Daniel

AU - Colombo, Fabrizio

AU - Lewkowicz, Izchak

AU - Sabadini, Irene

PY - 2018/10/1

Y1 - 2018/10/1

N2 - We first review realizations of Herglotz functions in the unit ball of CN and provide new insights. Then, we define the corresponding class and prove the extend the results in the case of several quaternionic variables.

AB - We first review realizations of Herglotz functions in the unit ball of CN and provide new insights. Then, we define the corresponding class and prove the extend the results in the case of several quaternionic variables.

KW - Gleason's problem

KW - Herglotz functions

KW - Several complex variables

KW - Several quaternionic variables

UR - http://www.scopus.com/inward/record.url?scp=85048534166&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2018.05.066

DO - 10.1016/j.jmaa.2018.05.066

M3 - Article

AN - SCOPUS:85048534166

SN - 0022-247X

VL - 466

SP - 169

EP - 182

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Herglotz functions of several quaternionic variables

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this