Abstract
We introduce a sharp trace Tr#
and a sharp determinant Det#(l−z
) for an algebra of operators
acting on functions of bounded variation on the real line. We show that the zeroes of the sharp determinant describe the discrete spectrum of
. 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.
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Oblatum 8-V-1995 & IX-1995
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Baladi, V., Ruelle, D. Sharp determinants. Invent. math. 123, 553–574 (1996). https://doi.org/10.1007/s002220050040
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DOI: https://doi.org/10.1007/s002220050040