Estimates for Sums of Eigenfunctions of Elliptic Pseudo-differential Operators on Compact Lie Groups

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...

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Bibliographic Details
Published in:The Journal of geometric analysis 2024-12, Vol.34 (12), Article 374
Main Authors: Cardona, Duván, Delgado, Julio, Ruzhansky, Michael
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Control theory
Convex and Discrete Geometry
Differential equations
Differential Geometry
Dynamical Systems and Ergodic Theory
Eigenvectors
Estimates
Fourier Analysis
Global Analysis and Analysis on Manifolds
Lie groups
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Summary: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.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-024-01760-0