Estimates for sums of eigenfunctions of elliptic pseudo-differential operators on compact Lie groups

2022/09/24 by Cardona, Duván, Delgado, Julio, Ruzhansky, Michael
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2209.12092

Abstract

We extend the estimates proved by Donnelly and Fefferman and by Lebeau and Robbiano 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 the control theory, we obtain the null-controllability for diffusion models for elliptic pseudo-differential operators on compact Lie groups.

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