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Theses
Extension of the canonical trace and associated determinants
Abstract : This thesis is devoted to the study of the canonical trace and two types of deter- minants: on the one hand a determinant associated with the canonical trace on a class of pseudodi erential operators and on the other hand determinants associated with regularized traces. In the rst part, in odd dimension, we revisit the uniqueness of the canonical trace on the space of classical pseudodi erential operators of odd class before ex- tending it to log-polyhomogeneous operators of odd class. We classify the traces on the algebra of classical pseudodi erential operators of odd class and order zero. In the second part, we establish the locality of the multiplicative anomaly of the weighted determinant and the zeta determinant. These results are obtained thanks to the study of the locality of the weighted trace of the operator L(A;B). We then derive from these results the local expression of the multiplicative anomalies in terms of the noncommutative residue. In the third part, we classify multiplicative determinants on the grounds of the classi cation of traces on classical pseudodi erential operators of odd class and order zero in odd dimension. We also de ne the symmetrized determinant obtained from the canonical trace applied to the symmetrized logarithm of an odd class operator in odd dimension. We show the multiplicativy of this determinant under some restrictions on the spectral cuts of the operators.
Cited literature [44 references]
https://tel.archives-ouvertes.fr/tel-00725230
Contributor : Camille Meyer <>
Submitted on : Friday, August 24, 2012 - 1:43:27 PM
Last modification on : Monday, September 14, 2020 - 1:30:02 PM
Long-term archiving on: : Friday, December 16, 2016 - 8:07:42 AM
Contributor : Camille Meyer <>
Submitted on : Friday, August 24, 2012 - 1:43:27 PM
Last modification on : Monday, September 14, 2020 - 1:30:02 PM
Long-term archiving on: : Friday, December 16, 2016 - 8:07:42 AM