Sharp determinants |
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Authors: | V Baladi D Ruelle |
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Institution: | (1) ETH Zürich, CH-8092 Zürich, Switzerland , CH;(2) Institut des Hautes études Scientifiques, F-91440 Bures-sur-Yvette, France; Fax: 33(1) 69 07 60 24, FR |
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Abstract: | We introduce a sharp trace Tr
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ℳ and a sharp determinant Det
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(1−z ℳ) for an algebra of operators ℳ acting on functions of bounded variation on the real line. We show that the zeroes of the sharp determinant describe the
discrete spectrum of ℳ. 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.
Oblatum 8-V-1995 & IX-1995 |
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Keywords: | |
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