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

Duván Cardona; Julio Delgado; Michael Ruzhansky

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arXiv · 2209.12092

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

Duván Cardona·Julio Delgado·Michael Ruzhansky

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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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Duván Cardona, Julio Delgado, Michael Ruzhansky. 2022-09-24. Estimates for sums of eigenfunctions of elliptic pseudo-differential operators on compact Lie groups. https://arxiv.org/abs/2209.12092

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