Abstract
In this paper we investigate the Dixmier trace and the noncommutative residue (also called Wodzicki’s residue) of pseudo-differential operators by using the notion of a global symbol. We consider both cases, compact manifolds with or without boundary. Our analysis on the Dixmier trace of invariant pseudo-differential operators on closed manifolds will be based on the Fourier analysis associated with every elliptic and positive operator and the quantization process developed by Delgado and Ruzhansky. In particular, for compact Lie groups, this can be done by using the representation theory of the group in view of the Peter–Weyl Theorem and the Ruzhansky–Turunen symbolic calculus. The analysis of invariant pseudo-differential operators on compact manifolds with boundary will be based on the global calculus of pseudo-differential operators developed by Ruzhansky and Tokmagambetov.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.