Boundary values of holomorphic functions and heat kernel method in translation-invariant distribution spaces

Abstract

We study boundary values of holomorphic functions in translation-invariant distribution spaces of type ${\mathcal{D}}_{E_{\ast }^{\prime }}^{\prime }$. New edge of the wedge theorems are obtained. The results are then applied to represent ${\mathcal{D}}_{E_{\ast }^{\prime }}^{\prime }$ as a quotient space of holomorphic functions. We also give representations of elements of ${\mathcal{D}}_{E_{\ast }^{\prime }}^{\prime }$ 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 ${\mathcal{D}}_{L^p}^{\prime }$, ${\mathcal{B}}^{\prime }$, and their weighted versions.

21 pages; with minor corrections

References in corpus (1)

• A General Integral

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