Uniqueness of the Kontsevich-Vishik Trace

Details Uniqueness of the Kontsevich-Vishik Trace Uniqueness of the Kontsevich-Vishik Trace

2007-02-09

arxiv.org/abs/math/0702250v1

Mathematics

Functional Analysis

Scientific paper

Let M be a closed manifold. We show that the Kontsevich-Vishik trace, which is defined on the set of all classical pseudodifferential operators on M, whose (complex) order is not an integer greater than or equal to -dim M, is the unique functional which (i) is linear on its domain, (ii) has the trace property and (iii) coincides with the L^2-operator trace on trace class operators. Also the extension to even-even pseudodifferential operators of arbitrary integer order on odd-dimensional manifolds and to even-odd pseudodifferential operators of arbitrary integer order on even-dimensional manifolds is unique.

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