Abstract
In this article we establish optimal estimates for the first eigenvalue of Schrödinger operators on the -dimensional unit sphere. These estimates depend on norms of the potential, or of its inverse, and are equivalent to interpolation inequalities on the sphere. We also characterize a semiclassical asymptotic regime and discuss how our estimates on the sphere differ from those on the Euclidean space.
Citation
Jean Dolbeault. Maria Esteban. Ari Laptev. "Spectral estimates on the sphere." Anal. PDE 7 (2) 435 - 460, 2014. https://doi.org/10.2140/apde.2014.7.435
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