Affordable Access

Publisher Website

Hilbert complexes

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
108
Issue
1
Identifiers
DOI: 10.1016/0022-1236(92)90147-b
Disciplines
  • Mathematics

Abstract

Abstract A Hilbert complex is just a complex 0 → D 0 → D 0 D 1 → D 1 ⋯ → D N − 1 D N → 0 , where the D j are closed operators between Hilbert spaces with domain D j and D j + 1 ∘ 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 we have in mind. In this paper we 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. We apply the abstract machinery to the de Rham complex in several singular situations.

There are no comments yet on this publication. Be the first to share your thoughts.