73 citations · 480 across the 42 of their papers we have counts for
50 papers
Dunkl approach to slice regular functions
Giulio Binosi, Hendrik De Bie, Pan Lian
In this paper, we establish a connection between Dunkl analysis and slice analysis in the setting of Clifford algebras. Specifically, we show that a Clifford algebra-valued functio…
On the radially deformed Fourier transform
Hendrik De Bie, Ze Yang
In this paper we consider the kernel of the radially deformed Fourier transform introduced in the context of Clifford analysis in [10]. By adapting the Laplace transform method fro…
Carleman estimates for higher step Grushin operators
Hendrik De Bie, Pan Lian
The higher step Grushin operators are a family of sub-elliptic operators which degenerate on a sub-manifold of . This paper establishes Carleman-type inequa…
Bounds for the kernel of the -generalized Fourier transform
Hendrik De Bie, Pan Lian, Frederick Maes
In this paper, we study the pointwise bounds for the kernel of the -generalized Fourier transform with , introduced by Ben Saïd, Kobayashi and Orsted. We present…
Superspace realizations of the Bannai-Ito algebra
N. Crampe, H. De Bie, P. Iliev +1
A model of the Bannai-Ito algebra in a superspace is introduced. It is obtained from the three-fold tensor product of the basic realization of the Lie superalgebra in te…
Generalised symmetries and bases for Dunkl monogenics
Hendrik De Bie, Alexis Langlois-Rémillard, Roy Oste +1
We introduce a family of commuting generalised symmetries of the Dunkl--Dirac operator inspired by the Maxwell construction in harmonic analysis. We use these generalised symmetrie…