## Analysis & PDE

• Anal. PDE
• Volume 7, Number 2 (2014), 435-460.

### Spectral estimates on the sphere

#### 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 $Lp$ 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.

#### Article information

Source
Anal. PDE, Volume 7, Number 2 (2014), 435-460.

Dates
Accepted: 13 June 2013
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.apde/1513731495

Digital Object Identifier
doi:10.2140/apde.2014.7.435

Mathematical Reviews number (MathSciNet)
MR3218815

Zentralblatt MATH identifier
1293.35183

#### Citation

Dolbeault, Jean; Esteban, Maria; Laptev, Ari. Spectral estimates on the sphere. Anal. PDE 7 (2014), no. 2, 435--460. doi:10.2140/apde.2014.7.435. https://projecteuclid.org/euclid.apde/1513731495

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