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Spectral properties of a class of operators associated with maps in one dimension

Published online by Cambridge University Press:  19 September 2008

David Ruelle
David Ruelle
Affiliation:
Institut des Hautes Etudes Scientifiques, 91440 Bures-sur-Yvette, France
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Abstract

Let f be a piecewise monotone map of the interval [0,1] to itself, and g a function of bounded variation on [0, 1]. Hofbauer, Keller and Rychlik have studied operators on functions of bounded variation, where

Among other things, they show that the essential spectral radius of is in many cases strictly smaller than the spectral radius; there exist therefore isolated eigenvalues of finite multiplicity. The purpose of the present paper is to prove similar results for a more general class of operators forming an algebra (and therefore containing sums of operators like ). An analogous extension was presented by Ruelle for operators associated with expanding maps.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 4 , December 1991 , pp. 757 - 767
Copyright
Copyright © Cambridge University Press 1991

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References

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