Traces on pseudodifferential operators and sums of commutators
Raphael Ponge (University of Toronto)
TL;DR
This paper provides elementary proofs for characterizations of traces on classical pseudodifferential operators across various orders and dimensions, unifying existing results with simple methods.
Contribution
It offers a unified, elementary approach to determine the space of traces on different classes of pseudodifferential operators, simplifying previous complex proofs.
Findings
Characterizations of traces on noninteger order PsiDOs.
Results on traces for integer order PsiDOs.
Descriptions of trace spaces for nonpositive order PsiDOs in various dimensions.
Abstract
The aim of this paper is to show that various known characterizations of traces on classical pseudodifferentials operators (PsiDOs) can actually be obtained by very elementary considerations on PsiDOs, using only basic properties of these operators. Thereby, we give a unified treatment of the determinations of the space of traces (i) on PsiDOs of noninteger orders or of regular parity-class, (ii) on integer order PsiDOs, (iii) on nonpositive order PsiDOs in dimension greather than or equal to 2, and (iv) on nonpositive order PsiDOs in dimension 1.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Operator Algebra Research · Spectral Theory in Mathematical Physics · Holomorphic and Operator Theory