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 Sd . We also prove a Berezin–Li–Yau inequality for domains contained in the hemisphere S+2 .
Lingua originale | Inglese |
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Numero di articolo | 280 |
Rivista | Journal of Geometric Analysis |
Volume | 33 |
Numero di pubblicazione | 9 |
DOI | |
Stato di pubblicazione | Pubblicato - set 2023 |