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Mathematical Sciences Publishers (MSP), Analysis & PDE, 2(7), p. 435-460

DOI: 10.2140/apde.2014.7.435

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Spectral estimates on the sphere

Journal article published in 2014 by Jean Dolbeault ORCID, Maria J. Esteban, Ari Laptev
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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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.