An extension of the theory of Fredholm determinants

  title={An extension of the theory of Fredholm determinants},
  author={David Ruelle},
  journal={Publications Math{\'e}matiques de l'Institut des Hautes {\'E}tudes Scientifiques},
  • D. Ruelle
  • Published 1 December 1990
  • Mathematics
  • Publications Mathématiques de l'Institut des Hautes Études Scientifiques
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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