Spectral estimates on the sphere

نویسندگان

  • JEAN DOLBEAULT
  • MARIA J. ESTEBAN
چکیده

In this article we establish optimal estimates for the first eigenvalue of Schrödinger operators on the d-dimensional unit sphere. These estimates depend on Lp 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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تاریخ انتشار 2013