Uniqueness of the Kontsevich-Vishik trace |
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Authors: | L Maniccia E Schrohe J Seiler |
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Institution: | Università di Bologna, Dipartimento di Matematica, Piazza di Porta S. Donato 5, 40127 Bologna, Italy ; Leibniz Universität Hannover, Institut für Analysis, Welfengarten 1, 30167 Hannover, Germany ; Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, Germany |
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Abstract: | Let be a closed manifold. We show that the Kontsevich-Vishik trace, which is defined on the set of all classical pseudodifferential operators on , whose (complex) order is not an integer greater than or equal to , is the unique functional which (i) is linear on its domain, (ii) has the trace property and (iii) coincides with the -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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Keywords: | Kontsevich-Vishik canonical trace pseudodifferential operators |
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