Subject: Mathematics - Functional Analysis
Subject: Mathematics - Functional Analysis
Subject: Mathematics - Complex Variables
Subject: 46F20, 46F15, 32A40

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Year: 2015

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Type: Article

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

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Author: Pavel Dimovski
Author: Stevan Pilipovic
Author: 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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Publisher: Informa UK Limited

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Relation: Complex Var. Elliptic Equ. 60 (2015), 1169-1189

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Identifier: oai:repository.ukim.mk:20.500.12188/3261
Identifier: http://hdl.handle.net/20.500.12188/3261
Identifier: 10.1080/17476933.2014.1002399
Identifier: http://www.tandfonline.com/doi/pdf/10.1080/17476933.2014.1002399
Identifier: 60
Identifier: 9

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