Boolean convolution in the quaternionic setting

Daniel Alpay; Marek Bozejko; Fabrizio Colombo; David P. Kimsey; Irene Sabadini

doi:10.1016/j.laa.2016.06.004

Boolean convolution in the quaternionic setting

Daniel Alpay
, Marek Bozejko
, Fabrizio Colombo
, David P. Kimsey
, Irene Sabadini

Department of Mathematics

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

2 Scopus citations

Abstract

In this paper we begin a study of free analysis in the quaternionic setting, and consider Boolean convolution for quaternion-valued measures. To this end we also study Boolean convolution for matrix-valued complex measures, also proving Boolean infinite divisibility and central limit theorems for these measures. Moreover we prove an integral representation for quaternionic Carathéodory and Herglotz functions.

Original language	English
Pages (from-to)	382-412
Number of pages	31
Journal	Linear Algebra and Its Applications
Volume	506
DOIs	https://doi.org/10.1016/j.laa.2016.06.004
State	Published - 1 Oct 2016

Keywords

Boolean convolution
Herglotz and Carathéodory functions
Matrix-valued measures
Quaternionic-valued measures

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.laa.2016.06.004

Cite this

@article{77396cd725f44993ac56c904c4a69015,

title = "Boolean convolution in the quaternionic setting",

abstract = "In this paper we begin a study of free analysis in the quaternionic setting, and consider Boolean convolution for quaternion-valued measures. To this end we also study Boolean convolution for matrix-valued complex measures, also proving Boolean infinite divisibility and central limit theorems for these measures. Moreover we prove an integral representation for quaternionic Carath{\'e}odory and Herglotz functions.",

keywords = "Boolean convolution, Herglotz and Carath{\'e}odory functions, Matrix-valued measures, Quaternionic-valued measures",

author = "Daniel Alpay and Marek Bozejko and Fabrizio Colombo and Kimsey, \{David P.\} and Irene Sabadini",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2016",

month = oct,

day = "1",

doi = "10.1016/j.laa.2016.06.004",

language = "English",

volume = "506",

pages = "382--412",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Boolean convolution in the quaternionic setting

AU - Alpay, Daniel

AU - Bozejko, Marek

AU - Colombo, Fabrizio

AU - Kimsey, David P.

AU - Sabadini, Irene

PY - 2016/10/1

Y1 - 2016/10/1

N2 - In this paper we begin a study of free analysis in the quaternionic setting, and consider Boolean convolution for quaternion-valued measures. To this end we also study Boolean convolution for matrix-valued complex measures, also proving Boolean infinite divisibility and central limit theorems for these measures. Moreover we prove an integral representation for quaternionic Carathéodory and Herglotz functions.

AB - In this paper we begin a study of free analysis in the quaternionic setting, and consider Boolean convolution for quaternion-valued measures. To this end we also study Boolean convolution for matrix-valued complex measures, also proving Boolean infinite divisibility and central limit theorems for these measures. Moreover we prove an integral representation for quaternionic Carathéodory and Herglotz functions.

KW - Boolean convolution

KW - Herglotz and Carathéodory functions

KW - Matrix-valued measures

KW - Quaternionic-valued measures

UR - https://www.scopus.com/pages/publications/84973573725

U2 - 10.1016/j.laa.2016.06.004

DO - 10.1016/j.laa.2016.06.004

M3 - Article

AN - SCOPUS:84973573725

SN - 0024-3795

VL - 506

SP - 382

EP - 412

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Boolean convolution in the quaternionic setting

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this