Transfer operators acting on Zygmund functions

Baladi, Viviane; Jiang, Yunping; Lanford, Oscar, III

doi:10.1090/S0002-9947-96-01599-1

Transfer operators acting on Zygmund functions
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by Viviane Baladi, Yunping Jiang and Oscar E. Lanford III PDF

Trans. Amer. Math. Soc. 348 (1996), 1599-1615 Request permission

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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