论文标题
半经典锥体操作员的分解和复杂的能力
Resolvents and complex powers of semiclassical cone operators
论文作者
论文摘要
我们对椭圆形半经典锥体差分运算符的分解和复杂功率进行统一描述，因为半经典参数$ h $倾向于$ 0 $。这样的操作员的一个例子是歧管$（x，g）$（x，g）$ dimension $ n \ geq 3 $带有锥形奇点的偏移$（x，g）上的转移的半经典laplacian $ h^2Δ_g+1 $。我们的方法是建设性的，基于几何微局部分析的技术：我们在适当分辨率的空间$ [0,1）_h \ times x \ times x \ times x $ $ h $相关的集成kernels;复合力的构建依赖于第二个半经典参数的演算。 As an application, we characterize the domains of $(h^2Δ_g+1)^{w/2}$ for $\mathrm{Re}\,w\in(-\frac{n}{2},\frac{n}{2})$ and use this to prove the propagation of semiclassical regularity through a cone point on a range of weighted semiclassical function空间。
We give a uniform description of resolvents and complex powers of elliptic semiclassical cone differential operators as the semiclassical parameter $h$ tends to $0$. An example of such an operator is the shifted semiclassical Laplacian $h^2Δ_g+1$ on a manifold $(X, g)$ of dimension $n\geq 3$ with conic singularities. Our approach is constructive and based on techniques from geometric microlocal analysis: we construct the Schwartz kernels of resolvents and complex powers as conormal distributions on a suitable resolution of the space $[0,1)_h\times X\times X$ of $h$-dependent integral kernels; the construction of complex powers relies on a calculus with a second semiclassical parameter. As an application, we characterize the domains of $(h^2Δ_g+1)^{w/2}$ for $\mathrm{Re}\,w\in(-\frac{n}{2},\frac{n}{2})$ and use this to prove the propagation of semiclassical regularity through a cone point on a range of weighted semiclassical function spaces.
