平移不变分布空间中全纯函数的边值与热核方法
Boundary values of holomorphic functions and heat kernel method in translation-invariant distribution spaces
摘要：
研究了$\mathcal{D}'_{E'_{\ast}}$型平移不变分布空间中全纯函数的边值问题。得到了新的楔边定理。然后将结果应用于表示$\mathcal{D}'_{E'_{\ast}}$作为全纯函数的商空间。我们还通过热核方法给出了$\mathcal{D}'_{E'_{\ast}}$的元素表示。我们的结果涵盖了特殊情况下的边界值，解析表示，和热核表示的背景下的施瓦兹空间$\mathcal{D}'_{L^{p}}$，$\mathcal{B}'$，和他们的加权版本。
英文摘要：
We study boundary values of holomorphic functions in translation-invariant distribution spaces of type $\mathcal{D}'_{E'_{\ast}}$. New edge of the wedge theorems are obtained. The results are then applied to represent $\mathcal{D}'_{E'_{\ast}}$ as a quotient space of holomorphic functions. We also give representations of elements of $\mathcal{D}'_{E'_{\ast}}$ via the heat kernel method. Our results cover as particular instances the cases of boundary values, analytic representations, and heat kernel representations in the context of the Schwartz spaces $\mathcal{D}'_{L^{p}}$, $\mathcal{B}'$, and their weighted versions.
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