Boundary values of cohomology classes as hyperfunctions
type: Item
instance of: scholarly article
title: Boundary values of cohomology classes as hyperfunctions
zbMATH Open document ID: 0847.32007
author: Paulo D. Cordaro
author: S. G. Gindikin
author: François Treves
published in: Journal of Functional Analysis
publication date: 1996-10-20T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/93308
review text: The authors consider hyperfunctions on a totally real submanifold \(X\) in \(\mathbb{C}^m\). They define the boundary value of a holomorphic-function coefficient cohomology class of degree \(q(0 \leq q \leq m - 1)\) in a wedge contained in \(\mathbb{C}^m\) whose edge lies on an arbitrary \(m\)-dimensional totally real submanifold \(X\). It is a hyperfunction on \(X\) and equivalent to use the Dolbeault or the Čech realization of the cohomology. If the directed cone of the wedge is convex, the boundary value map is injective. The corresponding spaces of germs of hyperfunctions are characterized by their hypo-analytic wave front set.
Mathematics Subject Classification ID: 32A45
Mathematics Subject Classification ID: 32A40
Mathematics Subject Classification ID: 46F15
zbMATH DE Number: 847463
zbMATH Keywords: boundary values of holomorphic functions
zbMATH Keywords: hyperfunctions
reviewed by: Masakazu Muro
MaRDI profile type: Publication
OpenAlex ID: W2111798813
DOI: 10.1006/JFAN.1995.1087
description: scientific article; zbMATH DE number 847463