论文标题
Hörmander-fock空间
A Hörmander-Fock space
论文作者
论文摘要
在最近的一篇论文中，我们在一个复杂变量中使用了$ 2 $的多序分析函数的基本分解属性来表征经典$ \ operline {\ partial} $的解决方案 - 给定的分析和多分析数据的问题。我们的方法提出了对我们称为Hörmander-fock空间的特殊复制核Hilbert空间的研究，该空间将在本文中进一步研究。该空间的主要属性以特定的力矩序列编码为$η=（η_n）_ {n \ geq 0} $，导致特殊的整个函数$ \ mathsf {e}（z）$，用于表达Hörmander-fock Space的Kernel功能。我们还提供了一个属于Alpay等人最近引入的ML类的特殊函数的示例。并将Bochner-Minlos型定理应用于此功能，从而激发了与随机过程理论的进一步联系。
In a recent paper we used a basic decomposition property of polyanalytic functions of order $2$ in one complex variable to characterize solutions of the classical $\overline{\partial}$-problem for given analytic and polyanalytic data. Our approach suggested the study of a special reproducing kernel Hilbert space that we call the Hörmander-Fock space that will be further investigated in this paper. The main properties of this space are encoded in a specific moment sequence denoted by $η=(η_n)_{n\geq 0}$ leading to a special entire function $\mathsf{E}(z)$ that is used to express the kernel function of the Hörmander-Fock space. We present also an example of a special function belonging to the class ML introduced recently by Alpay et al. and apply a Bochner-Minlos type theorem to this function, thus motivating further connections with the theory of stochastic processes.
