Pseudodifferential Operators and Regularized Traces
Matthias Lesch
备注：
38 pages, 1 figure; rewritten and revised according to the referee's suggestions, section on the Hilbert space trace added; accepted for publication in the Proceedings of the Conference on Motives, Quantum Field Theory and Pseudodifferential Operators, Boston, June 2008, Clay Mathematics Proceedings; v3 a few BUG fixes, none really serious, but one annoying omission fixed
发表信息：
In: Motives, Quantum Field Theory, and Pseudodifferential Operators, Clay Mathematics Proceedings, vol. 12, Amer. Math. Soc., Providence, RI, 2010, pp. 37-72
This paper is based on talks delivered in summer 2008 at the Conference on Motives, QFT and Pseudodifferential Operators in Boston, and at the Trimester programme Geometry and Physics, Hausdorff Institute for Mathematics in Bonn
The paper surveys the pseudodifferential calculus with parameter, resolvent expansions, Dixmier trace, noncommutative residue, Kontsevich-Vishik canonical trace as well some aspects of regularized integrals on spaces of symbols.
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In a previous paper we established Cwikel-type estimates on noncommutative tori and used them to get analogues in this setting of the Cwikel-Lieb-Rozenblum (CLR) and Lieb-Thirring inequalities for negative eigenvalues of fractional Schrödinger operators. In this paper, we focus on "curved" NC tori, where the role of the usual Laplacian is played by Laplace-Beltrami operators associated with arbitrary Riemannian metrics. The Cwikel-type estimates of our previous paper are extended to pseudodifferential operators and powers of Laplace-Beltrami operators. There are several applications of these e…
