# Semiclassical estimates for eigenvalue means of Laplacians on spheres

@inproceedings{Buoso2022SemiclassicalEF, title={Semiclassical estimates for eigenvalue means of Laplacians on spheres}, author={Davide Buoso and Paolo Luzzini and Luigi Provenzano and Joachim Stubbe}, year={2022} }

We compute three-term semiclassical asymptotic expansions of counting functions and Rieszmeans of the eigenvalues of the Laplacian on spheres and hemispheres, for both Dirichlet and Neumann boundary conditions. Specifically for Riesz-means we prove upper and lower bounds involving asymptotically sharp shift terms. We also prove a Berezin-Li-Yau inequality for domains contained in the hemisphere S+. Moreover, we consider polyharmonic operators for which we prove analogous results that highlight…

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