A partial converse to Hadamard's theorem on homeomorphisms.
type: Item
instance of: scholarly article
title: A partial converse to Hadamard's theorem on homeomorphisms.
zbMATH Open document ID: 1042.93033
published in: Circuits, Systems, and Signal Processing
publication date: 2002-01-01T00:00:00Z
review text: A theorem by Hadamard gives a two-part condition under which a map from one Banach space to another is a homeomorphism. The theorem, while often very useful, is incomplete in the sense that it does not explicitly specify the family of maps for which the condition is met. Here, under a typically weak additional assumption on the map, the author shows that Hadamard's condition is met if and only if the map is a homeomorphism with a Lipschitz continuous inverse. An application is given concerning the relation between the stability of a nonlinear system and the stability of related linear systems.
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 46T20
Mathematics Subject Classification ID: 47A50
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 47N70
Mathematics Subject Classification ID: 93B15
zbMATH DE Number: 1885801
author: Irwin W. Sandberg
MaRDI profile type: Publication
full work available at URL: s00034-004-7045-x
OpenAlex ID: W2027939923
DOI: 10.1007/S00034-004-7045-X
description: scientific article; zbMATH DE number 1885801