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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 $\mathbb{R}^{d}$.
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참고문헌 (27)
참고문헌 신청
A. Beurling / 1989 / The collect works of Arne Beurling / Birkhauser : 1 ~ 2
A. Bonami / 2002 / Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms / Rev. Mat. Iberoamericana 19 : 22 ~ 35
A. Miyachi / 1997 / A generalization of theorem of Hardy / Harmonic Analysis Seminar held at Izunagaoka : 44 ~ 51
B. Schapira / 2008 / Contributions to the hypergeometric function theory of Heckman and Opdam:sharpe stimates, Schwartz spaces, heat kernel / Geom. Funct. Anal 18 : 222 ~ 25
D. Slepian / 1961 / Prolate spheroidal wave functions, Fourier analysis and uncertainty I / Bell. Syst. Tech. J 40
A. Bonami / 2002 / Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms / Rev. Mat. Iberoamericana 19 : 22 ~ 35
A. Miyachi / 1997 / A generalization of theorem of Hardy / Harmonic Analysis Seminar held at Izunagaoka : 44 ~ 51
B. Schapira / 2008 / Contributions to the hypergeometric function theory of Heckman and Opdam:sharpe stimates, Schwartz spaces, heat kernel / Geom. Funct. Anal 18 : 222 ~ 25
D. Slepian / 1961 / Prolate spheroidal wave functions, Fourier analysis and uncertainty I / Bell. Syst. Tech. J 40
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