论文标题
最佳全体形态扩展的复杂嵌入，toeplitz操作员和传递性
Complex embeddings, Toeplitz operators and transitivity of optimal holomorphic extensions
论文作者
论文摘要
在带有固定正线束和子手机的复杂歧管的设置中，我们考虑了最佳的Ohsawa-Takegoshi扩展运算符，并在Submanifold上将线条束的全体形状部分发送到其在其环境流层上的最小$ l^2 $ -norm的环境流形上。我们表明，对于半经典环境中的子曼叶塔的塔，即当我们考虑线条束的巨大张量功率时，扩展操作员满足了传递性属性模型，一些小缺陷可以通过toeplitz型操作员表达。我们计算了此“传递性缺陷”的渐近扩展中的第一个重要项。作为副产品，我们推断出Toeplitz类型运算符，扩展和限制性操作员的组成规则，并在Ohsawa-Takegoshi扩展定理的半经典版本中计算最佳常数的渐近扩展中的第二项。
In a setting of a complex manifold with a fixed positive line bundle and a submanifold, we consider the optimal Ohsawa-Takegoshi extension operator, sending a holomorphic section of the line bundle on the submanifold to the holomorphic extension of it on the ambient manifold with the minimal $L^2$-norm. We show that for a tower of submanifolds in the semiclassical setting, i.e. when we consider a large tensor power of the line bundle, the extension operators satisfy transitivity property modulo some small defect, which can be expressed through Toeplitz type operators. We calculate the first significant term in the asymptotic expansion of this "transitivity defect". As a byproduct, we deduce the composition rules for Toeplitz type operators, the extension and restriction operators, and calculate the second term in the asymptotic expansion of the optimal constant in the semi-classical version of Ohsawa-Takegoshi extension theorem.
