Buoso, DavideLuzzini, PaoloProvenzano, LuigiStubbe, Joachim2023-07-172023-07-172023-07-172023-09-0110.1007/s12220-023-01326-6https://infoscience.epfl.ch/handle/20.500.14299/199181WOS:001016248800001We 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).Mathematicseigenvaluespolya's conjecturespheres and hemispheresriesz-meansberezin-li-yau inequalitykroger inequalityaveraged variational principlesemiclassical expansionsasymptotically sharp estimatessumsdomainstext::journal::journal article::research article