We prove generation results of analytic strongly continuous semigroups on \(L^p({{\mathbb {R}}}^d,{{\mathbb {R}}}^m)\) (\(1<p<\infty \)) for a class of vector-valued Schrödinger operators with unbounded coefficients. We also prove Gaussian type estimates for such semigroups.

中文翻译：

---

关于在$$ L ^ p $$ L p空间中具有无界扩散的向量值Schrödinger算子

我们证明了\（L ^ p（{{\ mathbb {R}}} ^ d，{{\ mathbb {R}}} ^ m）\）（\（1 <p <\ infty \））表示一类具有无穷系数的向量值Schrödinger算子。我们还证明了此类半群的高斯类型估计。