Segal-Bargmann transform: the q-deformation

被引：1

作者：

Cebron, Guillaume ^{[1
]}

Ho, Ching-Wei ^{[2
]}

机构：

[1] Univ Paul Sabatier, Inst Math Toulouse, 118 Route Narbonne, F-31062 Toulouse, France

[2] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2018年 / 108卷 / 07期

基金：

欧洲研究理事会;

关键词：

COMMUTATION RELATIONS; ANALYTIC-FUNCTIONS; BROWNIAN-MOTION; HILBERT-SPACE; OPERATORS;

D O I：

10.1007/s11005-017-1039-7

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We give identifications of the q-deformed Segal-Bargmann transform and define the Segal-Bargmann transform on mixed q-Gaussian variables. We prove that, when defined on the random matrix model of Sniady for the q-Gaussian variable, the classical Segal-Bargmann transform converges to the q-deformed Segal-Bargmann transform in the large N limit. We also show that the q-deformed Segal-Bargmann transform can be recovered as a limit of a mixture of classical and free Segal-Bargmann transform.

引用

页码：1677 / 1715

页数：39

共 50 条

[1] Segal–Bargmann transform: the q-deformation
Guillaume Cébron
Ching-Wei Ho
[J]. Letters in Mathematical Physics, 2018, 108 : 1677 - 1715
[2] Slice Segal-Bargmann transform
Cnudde, L.
De Bie, H.
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2017, 50 (25)
[3] Entropy and the Segal-Bargmann transform
Sontz, SB
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1998, 39 (04) : 2402 - 2417
[4] A Quaternionic Analogue of the Segal-Bargmann Transform
Diki, K.
Ghanmi, A.
[J]. COMPLEX ANALYSIS AND OPERATOR THEORY, 2017, 11 (02) : 457 - 473
[5] Uncertainty Principles for the Segal-Bargmann Transform
Fethi SOLTANI
[J]. Journal of Mathematical Research with Applications, 2017, 37 (05) : 563 - 576
[6] The Segal-Bargmann transform for Levy functionals
Lee, YJ
Shih, HH
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1999, 168 (01) : 46 - 83
[7] Perelomov problem and inversion of the Segal-Bargmann transform
Yu. A. Neretin
[J]. Functional Analysis and Its Applications, 2006, 40 : 330 - 333
[8] The Segal-Bargmann transform for path-groups
Hall, BC
Sengupta, AN
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 152 (01) : 220 - 254
[9] THE μ-DEFORMED SEGAL-BARGMANN TRANSFORM IS A HALL TYPE TRANSFORM
Bruce Sontz, Stephen
[J]. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2009, 12 (02) : 269 - 289
[10] A q-deformation of the true-polyanalytic Bargmann transform
Arjika, Sama
El Moize, Othmane
Mouayn, Zouhair
[J]. COMPTES RENDUS MATHEMATIQUE, 2018, 356 (08) : 903 - 910

← 1 2 3 4 5 →