论文标题
部分可观测时空混沌系统的无模型预测
Semi-classical asymptotics of partial Bergman kernels on $\mathbb{R}$-symmetric complex manifolds with boundary
论文作者
论文摘要
令$ m $为一个相对紧凑的连接开放子集，具有复杂歧管$ m'$的平滑连接边界。令$（l，h^l）\ rightarrow m'$为$ m'$的正线捆绑包。假设$ m'$允许holomorphic $ \ mathbb {r} $ - 保留$ m $的边界并提升至$ l $。我们建立了与$ \ Mathbb {r} $ - $ l $的高力量相对于高频傅立叶模式相关的部分伯格曼内核的渐近扩展。作为一个应用程序，我们建立了Fefferman's和Bell-Ligocka的$ \ Mathbb {r} $ - equivariant类似物的结果，即在$ \ Mathbb {C}^n $中的弱假单胞菌域之间的平稳延伸至Biholomormorthic Maps的边界。另一个应用程序涉及伪循环歧管的嵌入。
Let $M$ be a relatively compact connected open subset with smooth connected boundary of a complex manifold $M'$. Let $(L,h^L)\rightarrow M'$ be a positive line bundle over $M'$. Suppose that $M'$ admits a holomorphic $\mathbb{R}$-action which preserves the boundary of $M$ and lifts to $L$. We establish the asymptotic expansion of a partial Bergman kernel associated to a package of Fourier modes of high frequency with respect to the $\mathbb{R}$-action in the high powers of $L$. As an application, we establish an $\mathbb{R}$-equivariant analogue of Fefferman's and Bell-Ligocka's result about smooth extension up to the boundary of biholomorphic maps between weakly pseudoconvex domains in $\mathbb{C}^n$. Another application concerns the embedding of pseudoconcave manifolds.
