期刊
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
卷 29, 期 2, 页码 182-197出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.acha.2009.08.012
关键词
Riemannian manifold; Uncertainty principle; Dunkl operator
资金
- DFG
Based on a result of Rosier and Voit for ultraspherical polynomials, we derive an uncertainty principle for compact Riemannian manifolds M. The frequency variance of a function in L-2(M) is therein defined by means of the radial part of the Laplace-Beltrami operator. The proof of the uncertainty rests upon Dunkl theory. In particular, a special differential-difference operator is constructed which plays the role of a generalized root of the radial Laplacian. Subsequently, we prove with a family of Gaussian-like functions that the deduced uncertainty is asymptotically sharp. Finally, we specify in more detail the uncertainty principles for well-known manifolds like the d-dimensional unit sphere and the real projective space. (c) 2009 Elsevier Inc. All rights reserved.
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