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QUALITATIVE UNCERTAINTY PRINCIPLES FOR THE INVERSE OF THE HYPERGEOMETRIC FOURIER TRANSFORM
Mejjaoli, Hatem The Kangwon-Kyungki Mathematical Society 2015 한국수학논문집 Vol.23 No.1
In this paper, we prove an $L^p$ version of Donoho-Stark's uncertainty principle for the inverse of the hypergeometric Fourier transform on $\mathbb{R}^d$. Next, using the ultracontractive properties of the semigroups generated by the Heckman-Opdam Laplacian operator, we obtain an $L^p$ Heisenberg-Pauli-Weyl uncertainty principle for the inverse of the hypergeometric Fourier transform on $\mathbb{R}^d$.
SPECTRAL THEOREMS ASSOCIATED TO THE DUNKL OPERATORS
Mejjaoli, Hatem The Kangwon-Kyungki Mathematical Society 2016 한국수학논문집 Vol.24 No.4
In this paper, we characterize the support for the Dunkl transform on the generalized Lebesgue spaces via the Dunkl resolvent function. The behavior of the sequence of $L^p_k$-norms of iterated Dunkl potentials is studied depending on the support of their Dunkl transform. We systematically develop real Paley-Wiener theory for the Dunkl transform on ${\mathbb{R}}^d$ for distributions, in an elementary treatment based on the inversion theorem. Next, we improve the Roe's theorem associated to the Dunkl operators.