Results 11 to 20 of about 2,888 (114)
Dunkl convolution and elliptic regularity for Dunkl operators
Mathematische NachrichtenAbstractWe discuss in which cases the Dunkl convolution of distributions , possibly both with non‐compact support, can be defined and study its analytic properties. We prove results on the (singular‐)support of Dunkl convolutions. Based on this, we are able to prove a theorem on elliptic regularity for a certain class of Dunkl operators, called ...
Dominik Brennecken
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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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The Dunkl kernel and intertwining operator for dihedral groups
, 2020 Dunkl operators associated with finite reflection groups generate a commutative algebra of differential-difference operators. There exists a unique linear operator called intertwining operator which intertwines between this algebra and the algebra of ...
De Bie, Hendrik, Lian, Pan
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An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian [PDF]
, 2008 We introduce the so-called Clifford-Hermite polynomials in the framework of Dunkl operators, based on the theory of Clifford analysis. Several properties of these polynomials are obtained, such as a Rodrigues formula, a differential equation and an ...
De Bie, Hendrik
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Dunkl Hyperbolic Equations [PDF]
, 2008 We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.Comment: This is a
Mejjaoli, Hatem
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The Dunkl intertwining operator
Journal of Functional Analysis, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Maslouhi, M., Youssfi, E.H.
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The total angular momentum algebra related to the $\mathrm{S}_3$ Dunkl Dirac equation [PDF]
, 2017 We consider the symmetry algebra generated by the total angular momentum operators, appearing as constants of motion of the $\mathrm{S}_3$ Dunkl Dirac equation.
De Bie, Hendrik +2 more
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The Hahn superalgebra and supersymmetric Dunkl oscillator models
, 2013 A supersymmetric extension of the Hahn algebra is introduced. This quadratic superalgebra, which we call the Hahn superalgebra, is constructed using the realization provided by the Dunkl oscillator model in the plane, whose Hamiltonian involves ...
Genest, Vincent X. +3 more
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A Limit Relation for Dunkl-Bessel Functions of Type A and B [PDF]
, 2008 We prove a limit relation for the Dunkl-Bessel function of type $B_N$ with multiplicity parameters $k_1$ on the roots $\pm e_i$ and $k_2$ on $\pm e_i\pm e_j$ where $k_1$ tends to infinity and the arguments are suitably scaled.
Rösler, Margit, Voit, Michael
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A Bochner Theorem for Dunkl Polynomials [PDF]
, 2011 We establish an analogue of the Bochner theorem for first order operators of Dunkl type, that is we classify all such operators having polynomial solutions.
Vinet, Luc, Zhedanov, Alexei
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