论文标题
复杂域中的半经典gevrey操作员
Semiclassical Gevrey operators in the complex domain
论文作者
论文摘要
我们研究了半经典的gevrey pseudodivfertial算子，该操作员作用于整个全态函数的指数加权空间。此类运算符的符号是在综合相位空间的合适的I-Lagrangian Submanifolds上定义的gevrey函数，它们在同一gevrey类或在某些较大的空间中几乎散布到这些子手机的复杂社区。使用几乎全体形态的扩展，我们可以在所有Gevrey指数的自然加权空间的自然规模上获得此类操作员的统一实现，只要Gevrey Index为$ \ leq 2 $。
We study semiclassical Gevrey pseudodifferential operators, acting on exponentially weighted spaces of entire holomorphic functions. The symbols of such operators are Gevrey functions defined on suitable I-Lagrangian submanifolds of the complexified phase space, which are extended almost holomorphically in the same Gevrey class, or in some larger space, to complex neighborhoods of these submanifolds. Using almost holomorphic extensions, we obtain uniformly bounded realizations of such operators on a natural scale of exponentially weighted spaces of holomorphic functions for all Gevrey indices, with remainders that are optimally small, provided that the Gevrey index is $\leq 2$.
