Hilbert complexes
type: Item
instance of: scholarly article
title: Hilbert complexes
zbMATH Open document ID: 0826.46065
DOI: 10.1016/0022-1236(92)90147-B
published in: Journal of Functional Analysis
publication date: 1993-01-16T00:00:00Z
review text: A Hilbert complex is just a complex \[ 0\to {\mathcal D}_0@> D_0>> {\mathcal D_1}@> D_1>>\cdots @> D_{N- 1}>> {\mathcal D}_N\to 0, \] where the \(D_j\) are closed operators between Hilbert spaces with domain \({\mathcal D}_j\) and \(D_{j+ 1}\circ D_j= 0\). Although this is a fairly simple object, it reflects surprisingly much of the structure known from elliptic complexes on noncompact manifolds, the main application the authors have in mind. In this paper they undertake a systematic study of Hilbert complexes and their relationship with elliptic complexes. It turns out that this perspective gives a common structure to various known theorems along with generalizations and extensions. The authors apply the abstract machinery to the de Rham complex in several singular situations.
Mathematics Subject Classification ID: 46M20
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 55U05
Mathematics Subject Classification ID: 58A12
zbMATH DE Number: 89204
zbMATH Keywords: closed operators between Hilbert spaces
zbMATH Keywords: elliptic complexes on noncompact manifolds
zbMATH Keywords: Hilbert complexes
zbMATH Keywords: de Rham complex
author: Jochen Brüning
author: Matthias Lesch
MaRDI profile type: Publication
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full work available at URL: 0022-1236(92)90147-b
OpenAlex ID: W4210649459
description: scientific article; zbMATH DE number 89204