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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A remark on expanding maps


Authors: Kung Ching Chang and Shu Jie Li
Journal: Proc. Amer. Math. Soc. 85 (1982), 583-586
MSC: Primary 47H15; Secondary 58C15
DOI: https://doi.org/10.1090/S0002-9939-1982-0660608-4
MathSciNet review: 660608
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Abstract: In this paper we discuss the following problem stated by L. Nirenberg: Let $T$ be an expanding map $H \to H$ ($H$ is a Hilbert space) with $T(0) = 0$. Suppose $T$ maps a neighborhood of the origin onto a neighborhood of the origin. Does $T$ map $H$ onto $H$? We answer positively the problem when $T$ is differentiable.


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Keywords: Expanding map, Hadamard implicit function theorem, potential operator
Article copyright: © Copyright 1982 American Mathematical Society