Boundary values of holomorphic functions and heat kernel method in translation-invariant distribution spaces - Pavel Dimovski; Stevan Pilipovic; Jasson Vindas (Informa UK Limited, 2015)
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.
Keywords: Mathematics - Functional Analysis; Mathematics - Functional Analysis; Mathematics - Complex Variables; 46F20, 46F15, 32A40