Elements of \({\mathcal D}_{L^s}^{\prime (M_ p)}\) and \({\mathcal D}_{L^s}^{\prime (M_ p)}\) as boundary values of holomorphic functions
type: Item
instance of: scholarly article
title: Elements of \({\mathcal D}_{L^s}^{\prime (M_ p)}\) and \({\mathcal D}_{L^s}^{\prime (M_ p)}\) as boundary values of holomorphic functions
zbMATH Open document ID: 0891.46019
author: Stevan Pilipović
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-02-23T00:00:00Z
review text: The author deals with holomorphic function spaces whose elements have boundary values in spaces of distributions, ultradistributions, and infra-hyperfunctions and, conversely, with the boundary value representation of elements in the quoted generalized function spaces by holomorphic functions. By using a simple and powerful method based on almost analytic extension and Stokes' theorem as well as on Komatsu's method, the complete boundary value characterization for spaces of ultradistributions related to a non-quasianalytic sequence is put into evidence in the frame of three theorems based on five lemmas.
Mathematics Subject Classification ID: 46F20
zbMATH DE Number: 954709
zbMATH Keywords: holomorphic function spaces
zbMATH Keywords: boundary values in spaces of distributions
zbMATH Keywords: ultradistributions
zbMATH Keywords: infra-hyperfunctions
zbMATH Keywords: boundary value representation
zbMATH Keywords: almost analytic extension
zbMATH Keywords: Stokes' theorem
zbMATH Keywords: Komatsu's method
zbMATH Keywords: complete boundary value characterization
reviewed by: Petre P. Teodorescu
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0408
OpenAlex ID: W1971219159
DOI: 10.1006/JMAA.1996.0408
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description: scientific article; zbMATH DE number 954709