## Analysis & PDE

• Anal. PDE
• Volume 7, Number 7 (2014), 1639-1648.

### Resolvent estimates for the magnetic Schrödinger operator

Georgi Vodev

#### Abstract

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

$G = − Δ + i b ( x ) ⋅ ∇ + i ∇ ⋅ b ( x ) + V ( x )$

on $L2(ℝn)$, $n≥3$, where $b(x)$ and $V(x)$ are large magnetic and electric potentials, respectively.

#### Article information

Source
Anal. PDE, Volume 7, Number 7 (2014), 1639-1648.

Dates
Revised: 17 May 2014
Accepted: 30 June 2014
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.apde/1513731606

Digital Object Identifier
doi:10.2140/apde.2014.7.1639

Mathematical Reviews number (MathSciNet)
MR3293446

Zentralblatt MATH identifier
1304.47004

Subjects
Primary: 47A10: Spectrum, resolvent

#### Citation

Vodev, Georgi. Resolvent estimates for the magnetic Schrödinger operator. Anal. PDE 7 (2014), no. 7, 1639--1648. doi:10.2140/apde.2014.7.1639. https://projecteuclid.org/euclid.apde/1513731606

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