Sharp determinants
type: Item
instance of: scholarly article
title: Sharp determinants
zbMATH Open document ID: 0856.47005
author: Viviane Baladi
author: David Ruelle
published in: Inventiones Mathematicae
publication date: 1996-09-01T00:00:00Z
full work available at URL: https://eudml.org/doc/144359
review text: We introduce a sharp trace \(\text{Tr}^\# {\mathcal M}\) and a sharp determinant \(\text{Det}^\#(1- z{\mathcal M})\) for an algebra of operators \(\mathcal M\) acting on functions of bounded variation on the real line. We show that the zeroes of the sharp determinant describe the discrete spectrum of \(\mathcal M\). 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.
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 37C25
Mathematics Subject Classification ID: 37E99
zbMATH DE Number: 922462
zbMATH Keywords: sharp trace
zbMATH Keywords: sharp determinant
zbMATH Keywords: functions of bounded variation
zbMATH Keywords: discrete spectrum
zbMATH Keywords: weighted zeta functions of interval maps
zbMATH Keywords: Milnor-Thurston kneading determinants
MaRDI profile type: Publication
OpenAlex ID: W3192222692
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DOI: 10.1007/S002220050040
description: scientific article; zbMATH DE number 922462