73 citations · 480 across the 42 of their papers we have counts for
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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…
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…
The monogenic Hua-Radon transform and its inverse
Denis Constales, Hendrik De Bie, Teppo Mertens +1
The monogenic Hua-Radon transform is defined as an orthogonal projection on holomorphic functions in the Lie sphere. Extending the work of Sabadini and Sommen, J. Geom. Anal. 29 (2…
Dunkl intertwining operator for symmetric groups
Hendrik De Bie, Pan Lian
In this note, we express explicitly the Dunkl kernel and generalized Bessel functions of type by the Humbert's function , with one variable specified. The ob…
Plane wave formulas for spherical, complex and symplectic harmonics
Hendrik De Bie, Frank Sommen, Michael Wutzig
This paper is concerned with spherical harmonics, and two refinements thereof: complex harmonics and symplectic harmonics. The reproducing kernels of the spherical and complex harm…
Explicit formulas for the Dunkl dihedral kernel and the -generalized Fourier kernel
Denis Constales, Hendrik De Bie, Pan Lian
In this paper, a new method is developed to obtain explicit and integral expressions for the kernel of the -generalized Fourier transform for . In the case of dihedral…