Abstract
AbstractWe 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$${\mathbb {S}}^d$$Sd. We also prove a Berezin–Li–Yau inequality for domains contained in the hemisphere$${\mathbb {S}}^2_+$$S+2.
Funder
Università degli Studi di Roma La Sapienza
Publisher
Springer Science and Business Media LLC
Reference43 articles.
1. Bérard, P., Besson, G.: Spectres et groupes cristallographiques. II. Domaines sphériques. Ann. Inst. Fourier (Grenoble) 30(3), 237–248 (1980)
2. Berezin, F.A.: Covariant and contravariant symbols of operators. Izv. Akad. Nauk SSSR Ser. Mat. 36, 1134–1167 (1972)
3. Berger, M., Gauduchon, P., Mazet, E.: Le spectre d’une variété riemannienne (The spectrum of a Riemannian manifold) Lect. Notes Math. Springer, Cham (1971)
4. Buoso, D., Luzzini, P., Provenzano, L., Stubbe, J.: On the spectral asymptotics for the buckling problem. J. Math. Phys. 62(12), 18 (2021). (Paper No. 121501)
5. Buoso, D., Luzzini, P., Provenzano, L., Stubbe, J.: Semiclassical expansions and estimates for eigenvalue means of Laplacians on compact homogeneous spaces. In preparation (2023)
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