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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