Resolvent estimates for the magnetic Schrödinger operator. (English) Zbl 1304.47004

Vodev, Georgi

Anal. PDE 7, No. 7, 1639-1648 (2014).

Summary: We prove optimal high-frequency resolvent estimates for self-adjoint operators of the form \[ G=-\Delta+ib(x)\cdot\nabla+i\nabla\cdot b(x)+V(x) \] on \(L^2(\mathbb{R}^n)\), \(n\geq 3\), where \(b(x)\) and \(V(x)\) are large magnetic and electric potentials, respectively.

MSC:

47A10	Spectrum, resolvent
47B38	Linear operators on function spaces (general)
35J10	Schrödinger operator, Schrödinger equation

Keywords:

magnetic potential; resolvent estimates