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RIGIDITY OF CONTINUOUS COBOUNDARIES

Published online by Cambridge University Press:  01 September 1997

ANTHONY N. QUAS
ANTHONY N. QUAS
Affiliation:
Statistical Laboratory, Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1SB
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Abstract

We consider the functional equation F∘T−F=f, where T is a measure-preserving transformation and f is a continuous function. We show that if there is an L∞ function F which satisfies this equation, then F is constrained to satisfy a number of regularity conditions, and, in particular, if T is a one-sided Bernoulli shift, then we show that there is a continuous function F satisfying this equation. We show that this is not the case for the two-sided shift.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 5 , September 1997 , pp. 595 - 600
Copyright
© The London Mathematical Society 1997

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