Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-14T23:16:16.747Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)