Estimates for Sums of Eigenfunctions of Elliptic Pseudo-differential Operators on Compact Lie Groups
Volume
34
Publisher
DOI
10.1007/s12220-024-01760-0
Journal
Journal of Geometric Analysis
Issue
ISSN
1050-6926
Metadata
Show full item recordAbstract
We extend the estimates proved by Donnelly and Fefferman, and by Lebeau, Robbiano and Zuazua, for sums of eigenfunctions of the Laplacian (on a compact manifold) to estimates for sums of eigenfunctions of any positive and elliptic pseudo-differential operator of positive order on a compact Lie group. Our criteria are imposed in terms of the positivity of the corresponding matrix-valued symbol of the operator. As an application of these inequalities in control theory, we obtain the null-controllability for diffusion models for elliptic pseudo-differential operators on compact Lie groups.
Authors
Cardona, D; Delgado, J; Ruzhansky, MCollections
- Mathematics [1689]