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Hölder estimates for magnetic Schrödinger semigroups in $${\mathbb {R}}^{d}$$ R d from mirror coupling
Letters in Mathematical Physics ( IF 1.2 ) Pub Date : 2021-02-13 , DOI: 10.1007/s11005-021-01360-x
Oliver Fürst , Batu Güneysu

We use the mirror coupling of Brownian motion to show that under a \(\beta \in (0,1)\)-dependent Kato-type assumption on the possibly nonsmooth electromagnetic potential, the corresponding magnetic Schrödinger semigroup in \({\mathbb {R}}^d\) has a global \(L^{p}\)-to-\(C^{0,\beta }\) Hölder smoothing property for all \(p\in [1,\infty ]\); in particular, his all eigenfunctions are uniformly \(\beta \)-Hölder continuous. This result shows that the eigenfunctions of the Hamilton operator of a molecule in a magnetic field are uniformly \(\beta \)-Hölder continuous under weak \(L^q\)-assumptions on the magnetic potential.



中文翻译:

基于镜像耦合的$$ {\ mathbb {R}} ^ {d} $$ R d中的磁性Schrödinger半群的Hölder估计

我们使用布朗运动的镜像耦合来表明,在可能不光滑的电磁势的依赖于\(\ beta \ in(0,1)\)的Kato型假设下,\({\ mathbb {R}} ^ d \)具有全局\(L ^ {p} \)- to- \(C ^ {0,\ beta} \)所有\(p \ in [1,\ infty ] \) ; 特别是,他的所有本征函数是均匀\(\测试\) -Hölder连续。该结果表明,在磁场势的弱(L ^ q)假设下,分子的哈密顿算子在磁场中的本征函数是均匀的(β)-霍尔德连续的。

更新日期:2021-02-15
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