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Dunkl wavelets and applications to inversion of the Dunkl intertwining operator and its dual [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 We define and study Dunkl wavelets and the corresponding Dunkl wavelets transforms, and we prove for these transforms Plancherel and reconstruction formulas. We give as application the inversion of the Dunkl intertwining operator and its dual.
Abdellatif Jouini
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Nonlocal Operational Calculi for Dunkl Operators [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 The one-dimensional Dunkl operator $D_k$ with a non-negative parameter $k$, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of $D_k$, satisfying this condition is studied.
Ivan H. Dimovski, Valentin Z. Hristov
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Boundedness of Multidimensional Dunkl-Hausdorff Operators
Journal of Function Spaces, 2020 In the present paper, we introduce the multidimensional Dunkl-Hausdorff operator ℋκ and we give simple sufficient conditions so that these operators be bounded on the weighted lebesgue spaces Lκpℝn and in the Hardy space Hκ1ℝn associated with the Dunkl ...
Radouan Daher, Faouaz Saadi
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The Fractional Dunkl Laplacian: Definition and Harmonization via the Mellin Transform
Mathematics, 2023 In this paper, we extend the scope of the Tate and Ormerod Lemmas to the Dunkl setting, revealing a profound interconnection that intricately links the Dunkl transform and the Mellin transform.
Fethi Bouzeffour
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MULTI-TERM TIME-FRACTIONAL DERIVATIVE HEAT EQUATION FOR ONE-DIMENSIONAL DUNKL OPERATOR
Вестник КазНУ. Серия математика, механика, информатика, 2022 In this paper, we investigate the well-posedness for Cauchy problem for multi-term time-fractional heat equation associated with Dunkl operator. The equation under consideration includes a linear combination of Caputo derivatives in time with decreasing ...
D. Serikbaev
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A new aspect of generalized integral operator and an estimation in a generalized function theory
Advances in Difference Equations, 2021 In this paper we investigate certain integral operator involving Jacobi–Dunkl functions in a class of generalized functions. We utilize convolution products, approximating identities, and several axioms to allocate the desired spaces of generalized ...
Shrideh Al-Omari +2 more
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A NEW CHARACTERIZATION OF SYMMETRIC DUNKL AND \(q\)-DUNKL-CLASSICAL ORTHOGONAL POLYNOMIALS
Ural Mathematical Journal, 2023 In this paper, we consider the following \(\mathcal{L}\)-difference equation $$\Phi(x) \mathcal{L}P_{n+1}(x)=(\xi_nx+\vartheta_n)P_{n+1}(x)+\lambda_nP_{n}(x),\quad n\geq0,$$where \(\Phi\) is a monic polynomial (even), \(\deg\Phi\leq2\), \(\xi_n ...
Yahia Habbachi
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On the algebra of symmetries of Laplace and Dirac operators [PDF]
, 2018 We consider a generalization of the classical Laplace operator, which includes the Laplace-Dunkl operator defined in terms of the differential-difference operators associated with finite reflection groups called Dunkl operators.
De Bie, Hendrik +2 more
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Dunkl-Poisson Equation and Related Equations in Superspace
Mathematical Modelling and Analysis, 2015 In this paper, we investigate the Almansi expansion for solutions of Dunkl-polyharmonic equations by the 0-normalized system for the Dunkl-Laplace operator in superspace.
Hong Fen Yuan, Valery V. Karachik
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Lp Hardy's identities and inequalities for Dunkl operators
Advanced Nonlinear Studies, 2022 The main purpose of this article is to establish the Lp{L}^{p} Hardy’s identities and inequalities for Dunkl operator on any finite balls and the entire space RN{{\mathbb{R}}}^{N}. We also prove Hardy’s identities and inequalities on certain domains with
Wang Jianxiong
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