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arXiv · 1301.1210

Spectral estimates on the sphere

Jean Dolbeault·Maria J. Esteban·Ari Laptev
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Abstract

In this article we establish optimal estimates for the first eigenvalue of Schrödinger operators on the d-dimensional unit sphere. These estimates depend on Lebsgue's norms of the potential, or of its inverse, and are equivalent to interpolation inequalities on the sphere. We also characterize a semi-classical asymptotic regime and discuss how our estimates on the sphere differ from those on the Euclidean space.

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Jean Dolbeault, Maria J. Esteban, Ari Laptev. 2013-06-16. Spectral estimates on the sphere. https://doi.org/10.2140/apde.2014.7.435

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