Neira-Jiménez, Carolina and Ouedraogo, Marie F.
Classification of traces and associated determinants on odd-class operators in odd dimensions.
Preprintreihe der Fakultät Mathematik 10/2012,
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:||Monograph (Working Paper)|
|Institutions:|| Mathematics > Prof. Dr. Bernd Ammann|
|Keywords:||pseudodifferential operators; odd-class; trace; determinant; logarithm; regular Lie group|
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||No, this version has not been refereed yet (as with preprints)|
|Created at the University of Regensburg:||Yes|
|Deposited On:||22 May 2012 08:39|
|Last Modified:||22 May 2012 08:39|