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An extension of the theory of Fredholm determinants

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Abstract

Analytic functions are introduced, which are analogous to the Fredholm determinant, but may have only finite radius of convergence. These functions are associated with operators of the form ε μ(dω) ℒω, where ℒω φ(x) = ϕω(x). φ(ψω x), , φ belongs to a space of Hölder or Cr functions, ϕω is Hölder or Cr, and ψω is a contraction or a Cr contraction. The results obtained extend earlier results by Haydn, Pollicott, Tangerman and the author on zeta functions of expanding maps.

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  1. Institut des Hautes Etudes Scientifiques, 35, route de Chartres, 91440, Bures-sur-Yvette

    David Ruelle

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  1. David Ruelle
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Ruelle, D. An extension of the theory of Fredholm determinants. Publications Mathématiques de l’Institut des Hautes Scientifiques 72, 175–193 (1990). https://doi.org/10.1007/BF02699133

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  • DOI: https://doi.org/10.1007/BF02699133

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