Inversion formulas for the Dunkl-type Segal-Bargmann transform

被引：8

作者：

Soltani, Fethi ^{[1
]}

机构：

[1] Jazan Univ, Dept Math, Fac Sci, Jazan 45142, Saudi Arabia

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2015年 / 26卷 / 05期

关键词：

extremal functions; Dunkl-type Segal-Bargmann transform; Dunkl-type Fock spaces; 46E22; 32A36; 32A15; GENERALIZED FOCK SPACES; HILBERT-SPACE; REAL LINE; OPERATORS; KERNEL;

D O I：

10.1080/10652469.2015.1004331

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give the inverse of the Dunkl-type Segal-Bargmann transform as a limit of certain integral operators. An application to Tikhonov regularization on the Dunkl-type Fock spaces is given using the theory of reproducing kernel Hilbert spaces.

引用

页码：325 / 339

页数：15

共 50 条

[1] Plancherel and inversion formulas for the Dunkl-type Segal-Bargmann transform
Fethi Soltani
Meriem Nenni
ANNALI DELL'UNIVERSITA' DI FERRARA, 2025, 71 (1)
[2] Uncertainty Principles for the Dunkl-Type Segal-Bargmann Transform
Soltani, Fethi
COMPLEX ANALYSIS AND OPERATOR THEORY, 2017, 11 (03) : 475 - 490
[3] Uncertainty Principles for the Dunkl-Type Segal–Bargmann Transform
Fethi Soltani
Complex Analysis and Operator Theory, 2017, 11 : 475 - 490
[4] Dunkl-type Segal-Bargmann transform and its applications to some partial differential equations
Soltani, Fethi
Nenni, Meriem
GEORGIAN MATHEMATICAL JOURNAL, 2025, 32 (01) : 163 - 174
[5] Perelomov problem and inversion of the Segal-Bargmann transform
Yu. A. Neretin
Functional Analysis and Its Applications, 2006, 40 : 330 - 333
[6] Perelomov problem and inversion of the Segal-Bargmann transform
Neretin, Yu. A.
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2006, 40 (04) : 330 - 333
[7] Coherent states of the one-dimensional Dunkl oscillator for real and complex variables and the Segal-Bargmann transformation of Dunkl-type
Ghazouani, Sami
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2022, 55 (50)
[8] THE μ-DEFORMED SEGAL-BARGMANN TRANSFORM IS A HALL TYPE TRANSFORM
Bruce Sontz, Stephen
INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2009, 12 (02) : 269 - 289
[9] Slice Segal-Bargmann transform
Cnudde, L.
De Bie, H.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2017, 50 (25)
[10] Inversion formula and uncertainty inequalities for the Weinstein-type Segal-Bargmann transform
Soltani, Fethi
Saadi, Hanen
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2023, 34 (08) : 619 - 634

← 1 2 3 4 5 →