On the Fractional Dunkl-Laplacian

被引：2

作者：

Bouzeffour, Fethi ^{[1
]}

Jedidi, Wissem ^{[2
]}

机构：

[1] King Saud Univ, Coll Sci, Dept Math, POB 2455, Riyadh 11451, Saudi Arabia

[2] King Saud Univ, Dept Stat & OR, POB 2455, Riyadh 11451, Saudi Arabia

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2024年 / 27卷 / 01期

关键词：

Fractional calculus (primary); Dunkl operators; Special functions associated with root systems; Fractional Dunkl-Laplacian; RIESZ-POTENTIALS; MAXIMAL-FUNCTION; TRANSFORM; OPERATORS;

D O I：

10.1007/s13540-023-00225-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a novel approach to the fractional Dunkl-Laplacian within a framework derived from specific reflection symmetries in Euclidean spaces. Our primary contributions include pointwise formulas, Bochner subordination, and addressing an extension problem for the fractional Dunkl-Laplacian.

引用

页码：433 / 457

页数：25

共 35 条

[1] Dunkl-Schrodinger Operators
Amri, Bechir
Hammi, Amel
[J]. COMPLEX ANALYSIS AND OPERATOR THEORY, 2019, 13 (03) : 1033 - 1058
[2] On the fractional Bessel operator
Bouzeffour, F.
Garayev, M.
[J]. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2022, 33 (03) : 230 - 246
[3] Fractional supersymmetric quantum mechanics and lacunary Hermite polynomials
Bouzeffour, F.
Garayev, M.
[J]. ANALYSIS AND MATHEMATICAL PHYSICS, 2021, 11 (01)
[4] Fractional Supersymmetric Hermite Polynomials
Bouzeffour, Fethi
Jedidi, Wissem
[J]. MATHEMATICS, 2020, 8 (02)
[5] An extension problem related to the fractional Laplacian
Caffarelli, Luis
Silvestre, Luis
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) : 1245 - 1260
[6] Chaabane, 2021, ARXIV
[7] Cherednik I., 2005, LONDON MATH SOC LECT, V319
[8] Dai F., 2015, HARMONICS DUNKL TRAN
[9] Dunkl C. F., 2001, ENCYCL MATH, V81
[10] DIFFERENTIAL-DIFFERENCE OPERATORS ASSOCIATED TO REFLECTION GROUPS
DUNKL, CF
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 311 (01) : 167 - 183

← 1 2 3 4 →