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Transfer operators acting on Zygmund functions


Authors: Viviane Baladi, Yunping Jiang and Oscar E. Lanford III
Journal: Trans. Amer. Math. Soc. 348 (1996), 1599-1615
MSC (1991): Primary 47A10, 47B38, 58F03, 26A16
DOI: https://doi.org/10.1090/S0002-9947-96-01599-1
MathSciNet review: 1348856
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Abstract: We obtain a formula for the essential spectral radius $\rho _{\text{ess}}$ of transfer-type operators associated with families of $C^{1+\delta }$ diffeomorphisms of the line and Zygmund, or Hölder, weights acting on Banach spaces of Zygmund (respectively Hölder) functions. In the uniformly contracting case the essential spectral radius is strictly smaller than the spectral radius when the weights are positive.


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Additional Information

Viviane Baladi
Affiliation: ETH Zurich, CH-8092 Zurich, Switzerland (on leave from CNRS, UMR 128, ENS Lyon, France) \phantom{vb}
Address at time of publication: Mathématiques, Université de Genève, 1211 Geneva 24, Switzerland
Email: baladi@sc2a.unige.ch

Yunping Jiang
Affiliation: Department of Mathematics, Queens College, The City University of New York, Flushing, New York 11367-1597
Email: yunqc@qcunix.acc.qc.edu

Oscar E. Lanford III
Affiliation: ETH Zurich, CH-8092 Zurich, Switzerland
Email: lanford@math.ethz.ch

DOI: https://doi.org/10.1090/S0002-9947-96-01599-1
Received by editor(s): March 30, 1995
Additional Notes: Y. Jiang is partially supported by an NSF grant (contract DMS-9400974), and PSC-CUNY awards.
Article copyright: © Copyright 1996 American Mathematical Society