论文标题
沿子延伸的最佳全体形态喷气机的最佳全体形态扩展的渐近学
The asymptotics of the optimal holomorphic extensions of holomorphic jets along submanifolds
论文作者
论文摘要
我们研究了$ l^2 $ - 最佳的霍明型骨膜延伸的渐近型，与沿亚策略的高张量构量相关的holomorthic喷气机的渐近延伸。 更确切地说，对于复杂的歧管中的固定复杂的子手机，我们考虑了操作员，该操作员对于沿正线束的子手机的给定塑形射流将其与环境歧管相关联。当线束的张量功率趋于无穷大时，我们为该扩展操作员提供了明确的渐近公式。这是通过对扩展运营商和相关伯格曼投影仪的Schwartz内核进行仔细研究来完成的。它扩展了我们以前的结果，用于全态部分而不是喷气机。 作为一种应用，我们证明了两个天然规范在霍明型喷气空间上的渐近等等距：一种是由环境歧管引起的，另一个是由submanifold诱导的。
We study the asymptotics of the $L^2$-optimal holomorphic extensions of holomorphic jets associated with high tensor powers of a positive line bundle along submanifolds. More precisely, for a fixed complex submanifold in a complex manifold, we consider the operator which for a given holomorphic jet along the submanifold of a positive line bundle associates the $L^2$-optimal holomorphic extension of it to the ambient manifold. When the tensor power of the line bundle tends to infinity, we give an explicit asymptotic formula for this extension operator. This is done by a careful study of the Schwartz kernels of the extension operator and related Bergman projectors. It extends our previous results, done for holomorphic sections instead of jets. As an application, we prove the asymptotic isometry between two natural norms on the space of holomorphic jets: one induced from the ambient manifold and another from the submanifold.
