95-205 Baladi V., Ruelle D.

Sharp determinants (63K, AMSTeX) May 2, 95

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Abstract. We introduce a sharp trace $\trr^\# \MM$ and a sharp determinant $\dett^\# (1-z\MM)$ for an algebra of operators $\MM$ acting on functions of bounded variation on the real line. We show that the zeroes of the sharp determinant describe the discrete spectrum of $\MM$. The relationship with weighted zeta functions of interval maps and Milnor-Thurston kneading determinants is explained. This yields a result on convergence of the discrete spectrum of approximated operators. (This is a revised version of the paper.)

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