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arXiv · 1904.00693

Resolvent estimates for the magnetic Schrödinger operator in dimension $n \geq 2$

Cristóbal J. Meroño·Leyter Potenciano-Machado·Mikko Salo
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Abstract

It is well known that the resolvent of the free Schrödinger operator on weighted $L^2$ spaces has norm decaying like $λ^{-\frac{1}{2}}$ at energy $λ$. There are several works proving analogous high-frequency estimates for magnetic Schrödinger operators, with large long or short range potentials, in dimensions $n \geq 3$. We prove that the same estimates remain valid in all dimensions $n \geq 2$.

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Cristóbal J. Meroño, Leyter Potenciano-Machado, Mikko Salo. 2019-04-01. Resolvent estimates for the magnetic Schrödinger operator in dimension $n \geq 2$. https://doi.org/10.1007/s13163-019-00316-z

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