Results 1 to 10 of about 160 (141)
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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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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Advancing Fractional Riesz Derivatives through Dunkl Operators
Mathematics, 2023 The aim of this work is to introduce a novel concept, Riesz–Dunkl fractional derivatives, within the context of Dunkl-type operators. A particularly noteworthy revelation is that when a specific parameter κ equals zero, the Riesz–Dunkl fractional ...
Fethi Bouzeffour
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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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Dunkl–Schrödinger Operators [PDF]
Complex Analysis and Operator Theory, 2018 In this paper, we consider the Schr dinger operators $L_k=- _k+V$, where $ _k$ is the Dunkl-Laplace operator and $V$ is a non-negative potential on $R^d$. We establish that $L_k $ is essentially self-adjoint on $C_0^\infty$. In particular, we develop a bounded $H^\infty$-calculus on $L^p$ spaces for the Dunkl harmonic oscillator operator.
Amri, Béchir, Hammi, Amel
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Dunkl operators for arbitrary finite groups [PDF]
Advances in Operator Theory, 2021 New example using Cuntz algebras, final version, 44 ...
Micho Đurđevich, Stephen Bruce Sontz
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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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Generalized Dunkl operator [PDF]
Ufimskii Matematicheskii Zhurnal, 2014 In the paper we introduce a generalized Dunkl operator acting in the space of entire functions on C. We study problems of harmonic analysis related with this operator and show its connection with the Gelfond-Leont'ev operator of generalized differentiation.
Il'mir Irshatovich Karamov +1 more
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