We compute three-term semiclassical asymptotic expansions of counting functions and Riesz-means 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, and we extend them to domains of S-d. We also prove a Berezin-Li-Yau inequality for domains contained in the hemisphere S-+(2).
Semiclassical Estimates for Eigenvalue Means of Laplacians on Spheres
Luzzini, Paolo;
2023
Abstract
We compute three-term semiclassical asymptotic expansions of counting functions and Riesz-means 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, and we extend them to domains of S-d. We also prove a Berezin-Li-Yau inequality for domains contained in the hemisphere S-+(2).
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