Baladi V., Ruelle D.
Sharp determinants
(63K, AMSTeX)

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.)