论文标题
Berezin-toeplitz操作员的异国表现
An exotic calculus of Berezin-Toeplitz operators
论文作者
论文摘要
我们开发了一个berezin-toeplitz运算符的演算，该计算量量化了紧凑型kähler歧管上的平滑功能的外来类别类别，并作用于正线捆绑包的荷兰形态段。这些功能（经典可观察物）是异国情调的，因为它们的导数被允许以局部几何形状和线条束的力量控制的方式生长。通过使用Melin和Sjöstrand的复杂固定相的方法对操作员的内核进行仔细分析来获得此量化的性能。我们获得了该较大类功能的功能性演算结果，痕量公式和参数结构。这些结果至关重要地用于证明概率的Weyl-law用于随机扰动（标准）berezin-toeplitz操作员。
We develop a calculus of Berezin-Toeplitz operators quantizing exotic classes of smooth functions on compact Kähler manifolds and acting on holomorphic sections of powers of positive line bundles. These functions (classical observables) are exotic in the sense that their derivatives are allowed to grow in ways controlled by local geometry and the power of the line bundle. The properties of this quantization are obtained via careful analysis of the kernels of the operators using Melin and Sjöstrand's method of complex stationary phase. We obtain a functional calculus result, a trace formula, and a parametrix construction for this larger class of functions. These results are crucially used in proving a probabilistic Weyl-law for randomly perturbed (standard) Berezin-Toeplitz operators.
