Non-commutative functions and the non-commutative free Levy-Hincin formula

被引：21

作者：

Popa, Mihai ^{[1
,2
]}

Vinnikov, Victor ^{[3
]}

机构：

[1] Ben Gurion Univ Negev, Ctr Adv Studies Math, IL-84105 Beer Sheva, Israel

[2] Romanian Acad, Inst Math, RO-70700 Bucharest, Romania

[3] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

来源：

ADVANCES IN MATHEMATICS | 2013年 / 236卷

关键词：

Free probability; R-transform; Non-commutative functions; Fully matricial functions; Infinite divisibility; INFINITE-DIVISIBILITY; LIMIT-THEOREMS; INDEPENDENCE; PRODUCTS;

D O I：

10.1016/j.aim.2012.12.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper is discussing infinite divisibility in the setting of operator-valued boolean, free and, more general, c-free independences. Particularly, using Hilbert bimodule and non-commutative function techniques, we obtain analogues of the Levy-Hincin integral representation for infinitely divisible real measures. (c) 2013 Elsevier Inc. All rights reserved.

引用

页码：131 / 157

页数：27

共 50 条

[1] ON THE LEVY-HINCIN FORMULA FOR COMMUTATIVE HYPERGROUPS
LASSER, R
[J]. LECTURE NOTES IN MATHEMATICS, 1984, 1064 : 298 - 308
[2] A non-commutative binomial formula
Rosengren, H
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2000, 32 (04) : 349 - 363
[3] Non-commutative automorphisms of bounded non-commutative domains
McCarthy, John E.
Timoney, Richard M.
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2016, 146 (05) : 1037 - 1045
[4] Testing non-commutative QED, constructing non-commutative MHD
Guralnik, Z
Jackiw, R
Pi, SY
Polychronakos, AP
[J]. PHYSICS LETTERS B, 2001, 517 (3-4) : 450 - 456
[5] On polynomial functions on non-commutative groups
Almira, J. M.
Shulman, E. V.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 458 (01) : 875 - 888
[6] NON-COMMUTATIVE CURVES AND THEIR ZETA FUNCTIONS
Jorgensen, Peter
[J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2002, 1 (02) : 175 - 199
[7] Non-commutative Chern-Simons terms and the non-commutative vacuum
Polychronakos, AP
[J]. JOURNAL OF HIGH ENERGY PHYSICS, 2000, (11):
[8] ELEMENTS OF NON-COMMUTATIVE PROBABILITY THEORY AND NON-COMMUTATIVE ERGODIC THEORY
SINAI, YG
[J]. THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1971, 16 (03): : 564 - &
[9] Non-commutative probability and non-commutative processes: Beyond the Heisenberg algebra
Mendes, R. Vilela
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2019, 60 (09)
[10] Free Probability and Non-commutative Symmetries
Speicher, Roland
[J]. QUANTUM SYMMETRIES, 2017, 2189 : 5 - 35

← 1 2 3 4 5 →