Jimenez, Carolina Neira and Ouedraogo, Marie Francoise (2012) Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimension. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 8: 023. ISSN 1815-0659,
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To supplement the already known classification of traces on classical pseudodifferential operators, we present a classification of traces on the algebras of odd-class pseudodifferential operators of non-positive order acting on smooth functions on a closed odd-dimensional manifold. By means of the one to one correspondence between continuous traces on Lie algebras and determinants on the associated regular Lie groups, we give a classification of determinants on the group associated to the algebra of odd-class pseudodifferential operators with fixed non-positive order. At the end we discuss two possible ways to extend the definition of a determinant outside a neighborhood of the identity on the Lie group associated to the algebra of odd-class pseudodifferential operators of order zero.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PSEUDODIFFERENTIAL-OPERATORS; NONCOMMUTATIVE RESIDUE; UNIQUENESS; FORMULA; pseudodifferential operators; odd-class; trace; determinant; logarithm; regular Lie group |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 25 May 2020 07:10 |
| Last Modified: | 25 May 2020 07:10 |
| URI: | https://pred.uni-regensburg.de/id/eprint/19494 |
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