论文标题
Hörmander's$ l^2 $ -Method，$ \ bar {\ partial} $ - 问题和多序函数理论在一个复杂变量中
Hörmander's $L^2$-method, $\bar{\partial}$-problem and polyanalytic function theory in one complex variable
论文作者
论文摘要
在本文中，我们考虑经典的$ \ bar {\ partial} $ - 在一个用于分析和多序数据的复杂变量的情况下。我们应用了多架函数的分解属性，以构建此问题的特定解决方案，并使用Cauchy-Riemann运算符的合适功率获得新的Hörmander型估计。我们还计算了$ \ bar {\ partial} $的特定解决方案 - 特定的多芯片数据（例如Itô综合性Hermite多项式和多芯片分析fock bernels）的问题。
In this paper we consider the classical $\bar{\partial}$-problem in the case of one complex variable both for analytic and polyanalytic data. We apply the decomposition property of polyanalytic functions in order to construct particular solutions of this problem and obtain new Hörmander type estimates using suitable powers of the Cauchy-Riemann operator. We also compute particular solutions of the $\bar{\partial}$-problem for specific polyanalytic data such as the Itô complex Hermite polynomials and polyanalytic Fock kernels.
