Resolvent estimates for the magnetic Schrödinger operator

Recent Issues

The Journal

ISSN: 1948-206X (e-only)

ISSN: 2157-5045 (print)

Vol. 7 (2014), No. 7, 1639–1648

DOI: 10.2140/apde.2014.7.1639

We prove optimal high-frequency resolvent estimates for self-adjoint operators of the form

G = - Δ + i b (x) \cdot \nabla + i \nabla \cdot b (x) + V (x)

on $L^{2} (ℝ^{n})$ , $n \geq 3$ , where $b (x)$ and $V (x)$ are large magnetic and electric potentials, respectively.

magnetic potential, resolvent estimates

Primary: 47A10

Received: 2 January 2014

Revised: 17 May 2014

Accepted: 30 June 2014

Published: 12 December 2014

Georgi Vodev
Département de Mathématiques, UMR 6629 du CNRS Université de Nantes 2, rue de la Houssiniere, BP 92208 44332 Nantes Cedex 03 France