PuSH - Publication Server of Helmholtz Zentrum München

Erb, W.

Uncertainty principles on compact Riemannian manifolds.

Appl. Comput. Harmon. Anal. 29, 182-197 (2010)
DOI
Open Access Green as soon as Postprint is submitted to ZB.
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.
Altmetric
Additional Metrics?
[➜Log in]
Edit extra informations Login
Publication type Article: Journal article
Document type Scientific Article
Corresponding Author
Keywords Riemannian manifold; Uncertainty principle; Dunkl operator
ISSN (print) / ISBN 1063-5203
e-ISSN 1096-603X
Journal Applied and Computational Harmonic Analysis
Quellenangaben Volume: 29, Issue: 2, Pages: 182-197 Article Number: , Supplement: ,
Publisher Academic Press
Publishing Place San Diego, Calif. [u.a.]
Non-patent literature Publications
Reviewing status Peer reviewed
Institute(s) Institute of Biomathematics and Biometry (IBB)