%0 Journal Article
%T Boundary values of holomorphic functions and heat kernel method in translation-invariant distribution spaces
%A Pavel Dimovski
%A Stevan Pilipovic
%A Jasson Vindas
%J Mathematics
%D 2014
%I arXiv
%R 10.1080/17476933.2014.1002399
%X 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.
%U http://arxiv.org/abs/1409.0197v2