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arXiv · 1409.0197

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

Pavel Dimovski·Stevan Pilipovic·Jasson Vindas
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Abstract

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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Pavel Dimovski, Stevan Pilipovic, Jasson Vindas. 2015-02-22. Boundary values of holomorphic functions and heat kernel method in translation-invariant distribution spaces. https://doi.org/10.1080/17476933.2014.1002399

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