Wednesday, March 13, 2013

1303.2979 (Hendrik De Bie)

The kernel of the radially deformed Fourier transform    [PDF]

Hendrik De Bie
The radially deformed Fourier transform, introduced in [S. Ben Said, T. Kobayashi and B. Orsted, Laguerre semigroup and Dunkl operators, Compositio Math.], is an integral transform that depends on a numerical parameter $a \in R^{+}$. So far, only for $a=1$ and $a=2$ the kernel of this integral transform is determined explicitly. In the present paper, explicit formulas for the kernel of this transform are obtained when the dimension is even and $a = 2/n$ with $n \in N$. As a consequence, it is shown that the integral kernel is bounded in dimension 2.
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