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

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
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