Semiclassical Estimates for Eigenvalue Means of Laplacians on Spheres

Davide Buoso; Paolo Luzzini; Luigi Provenzano; Joachim Stubbe

doi:10.1007/s12220-023-01326-6

Semiclassical Estimates for Eigenvalue Means of Laplacians on Spheres

Davide Buoso
, Paolo Luzzini
, Luigi Provenzano
, Joachim Stubbe

Department of Sustainable Development and Ecological Transition

Research output: Contribution to journal › Article › peer-review

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 .

Original language	English
Article number	280
Journal	Journal of Geometric Analysis
Volume	33
Issue number	9
DOIs	https://doi.org/10.1007/s12220-023-01326-6
Publication status	Published - Sept 2023

Keywords

Asymptotically sharp estimates
Averaged variational principle
Berezin–Li–Yau inequality
Eigenvalues
Kröger inequality
Pólya’s conjecture
Riesz-means
Semiclassical expansions
Spheres and hemispheres

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10.1007/s12220-023-01326-6

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title = "Semiclassical Estimates for Eigenvalue Means of Laplacians on Spheres",

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 .",

keywords = "Asymptotically sharp estimates, Averaged variational principle, Berezin–Li–Yau inequality, Eigenvalues, Kr{\"o}ger inequality, P{\'o}lya{\textquoteright}s conjecture, Riesz-means, Semiclassical expansions, Spheres and hemispheres",

author = "Davide Buoso and Paolo Luzzini and Luigi Provenzano and Joachim Stubbe",

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T1 - Semiclassical Estimates for Eigenvalue Means of Laplacians on Spheres

AU - Buoso, Davide

AU - Luzzini, Paolo

AU - Provenzano, Luigi

AU - Stubbe, Joachim

PY - 2023/9

Y1 - 2023/9

N2 - 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 .

AB - 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 .

KW - Asymptotically sharp estimates

KW - Averaged variational principle

KW - Berezin–Li–Yau inequality

KW - Eigenvalues

KW - Kröger inequality

KW - Pólya’s conjecture

KW - Riesz-means

KW - Semiclassical expansions

KW - Spheres and hemispheres

UR - https://www.scopus.com/pages/publications/85162897324

U2 - 10.1007/s12220-023-01326-6

DO - 10.1007/s12220-023-01326-6

M3 - Article

SN - 1050-6926

VL - 33

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 9

M1 - 280

ER -

Semiclassical Estimates for Eigenvalue Means of Laplacians on Spheres

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Keywords

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