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

中文翻译：

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尺寸为$$ \ ge 2 $$≥2的Schrödinger磁性算子的溶剂估计

众所周知，自由Schrödinger算子在加权\（L ^ 2 \）空间上的分解在能量\（\ lambda处）的模衰减像\（\ lambda ^ {-\ frac {1} {2}} \\）\）。有几篇著作证明了对于具有大的长或短范围电势的磁性Schrödinger算符的高频估计，其尺寸为\（n \ ge 3 \）。我们证明了相同的估计在所有维度\（n \ ge 2 \）上仍然有效。