Resolvents and complex powers of semiclassical cone operators
Resolvents and complex powers of semiclassical cone operators
复制标题
半经典锥算子的分解和复幂
作者：
P. Hintz
当半经典参数h趋于0时，我们给出了椭圆半经典锥微分算子的预解式和复幂的统一描述。这类算子的一个例子是具有二次奇性的n维流形(X，g)$(X，g)$(X，g)$上的移位半经典拉普拉斯算子H2Δg+1$h^2\Delta_g+1$。n≥3$n\ge 3$。我们的方法是构造性的，并基于几何微局部分析的技巧：我们将预解器和复幂的Schwartz核构造为h-依赖积分核的空间[0，1)h×X×X$[0，1)_h\×X\乘X$的适当分辨率上的余正态分布；复幂的构造依赖于具有第二个半经典参数的微积分。作为应用，我们刻画了(h2Δg+1)w/2${\BIG(h^2\Delta_g+1\BIG)}^{w/2}$对REW∈−n2，n2$算子名{Re}w\in\Left(-\tfrac{n}{2}\tfrac{n}{2}\Right)$的整环，并用它证明了半经典正则性在一系列加权半经典函数空间上通过一个锥点的传播.
We give a uniform description of resolvents and complex powers of elliptic semiclassical cone differential operators as the semiclassical parameter h tends to 0. An example of such an operator is the shifted semiclassical Laplacian h2Δg+1$h^2\Delta _g+1$ on a manifold (X,g)$(X,g)$ of dimension n≥3$n\ge 3$ 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×X×X$[0,1)_h\times X\times X$ 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 (h2Δg+1)w/2${\big (h^2\Delta _g+1\big )}^{w/2}$ for Rew∈−n2,n2$\operatorname{Re}w\in \left(-\tfrac{n}{2},\tfrac{n}{2}\right)$ and use this to prove the propagation of semiclassical regularity through a cone point on a range of weighted semiclassical function spaces.
DOI：
10.1512/iumj.2014.63.5435
发表时间：
2013-07
期刊：
arXiv: Analysis of PDEs
影响因子：
--
作者：
R. Mazzeo;Boris Vertman
通讯作者：
R. Mazzeo;Boris Vertman
产品锥体上的辐射场
影响因子：
1.7
作者：
Baskin, Dean;Marzuola, Jeremy L.
通讯作者：
Marzuola, Jeremy L.