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Dunkl operators: Theory and applications
, 2018 These lecture notes are intended as an introduction to the theory of rational Dunkl operators and the associated special functions, with an emphasis on positivity and asymptotics. We start with an outline of the general concepts: Dunkl operators, the intertwining operator, the Dunkl kernel and the Dunkl transform.
Rosler, M., Koelink, Erik
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The Z(2)(n) Dirac-Dunkl operator and a higher rank Bannai-Ito algebra [PDF]
, 2016 De Bie, Hendrik +2 more
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PROPERTIES OF THE GENERALIZED DUNKL OPERATOR [PDF]
Вестник Башкирского университета, 2018 A. I. Rakhimova, V. V. Napalkov
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Dunkl Processes and Intertwining Operators
Dunkl Processes and Intertwining Operatorsapplication ...
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The Dunkl-Hausdorff operators and the Dunkl continuous wavelets transform
Journal of Pseudo-Differential Operators and Applications, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Radouan Daher, Faouaz Saadi
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Dunkl multiplier operators and applications
Integral Transforms and Special Functions, 2014We study some class of Dunkl multiplier operators; and we establish for them some versions of uncertainty principles. For these operators we give also an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev–Dunkl spaces.
Fethi Soltani
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Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators
Integral Transforms and Special Functions, 2002We use the Dunkl intertwining operator V_k and its dual ^tV_k to prove a Paley-Wiener theorem for the Dunkl transform, for functions and distributions, and geometric forms of this theorem. These operators permit also to define and study Dunkl translation operators and Dunkl convolution product.
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On the representing measures of Dunkl’s intertwining operator
Journal of Approximation Theory, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jiaxi Jiu, Zhongkai Li
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Journal of the Physical Society of Japan, 1995
Summary: The Dunkl operator is constructed based on the Yang-Baxter equation. We regard the \(R\)- and \(K\)-matrix,which satisfy the Yang-Baxter equation and th boundary Yang-Baxter equation,as operators acting on the functional space.In terms of these \(R\)- and \(K\)-operators acting on the functional space.In terms of these \(R\)- and \(K ...
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Summary: The Dunkl operator is constructed based on the Yang-Baxter equation. We regard the \(R\)- and \(K\)-matrix,which satisfy the Yang-Baxter equation and th boundary Yang-Baxter equation,as operators acting on the functional space.In terms of these \(R\)- and \(K\)-operators acting on the functional space.In terms of these \(R\)- and \(K ...
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Boundedness of the Dunkl–Hausdorff operator in Lebesgue spaces
Rocky Mountain Journal of Mathematics, 2021In this paper, the authors characterized the \(L^{p}_{\nu}(\mathbb{R})\)-boundedness of the so-called Dunkl-Hausdorff operator, i.e. \[ H_{\alpha, \phi}f(x)=\int_{\mathbb{R}}\frac{|\phi(t)|}{|t|^{2\alpha+2}} f\left(\frac{x}{t}\right)\, \mathrm{d}t, \] where the weight is given by \(\nu(x)=|x|^{2\alpha+1}\) and ...
Jain S., Fiorenza A., Jain P.
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