We demonstrate a parametrix construction, together with associated pseudodifferential operator calculus, for an operator of sum-of-squares type with semiclassical parameter. The form of operator we consider includes the generator of kinetic Brownian motion on the cosphere bundle of a Riemannian manifold. Regularity estimates in semiclassical Sobolev spaces are proven by establishing mapping properties for the parametrix.

中文翻译：

---

半经典亚椭圆算子的参数

我们演示了一个参数构造，以及相关的伪微分算子演算，用于具有半经典参数的平方和类型的算子。我们考虑的算子形式包括在黎曼流形的共球丛上产生动力学布朗运动的发生器。通过为参数建立映射属性来证明半经典 Sobolev 空间中的正则性估计。