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Rigidity of Continuous Coboundaries
Author(s) -
Quas Anthony N.
Publication year - 1997
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609396002810
Subject(s) - mathematics , bernoulli's principle , rigidity (electromagnetism) , transformation (genetics) , function (biology) , functional equation , continuous function (set theory) , mathematics subject classification , pure mathematics , mathematical analysis , differential equation , biochemistry , chemistry , structural engineering , evolutionary biology , biology , engineering , gene , aerospace engineering
We consider the functional equation F o 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. 1991 Mathematics Subject Classification 28D05, 58F11.