Levy, Cyril and Jimenez, Carolina Neira and Paycha, Sylvie (2016) THE CANONICAL TRACE AND THE NONCOMMUTATIVE RESIDUE ON THE NONCOMMUTATIVE TORUS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 368 (2). pp. 1051-1095. ISSN 0002-9947, 1088-6850
Full text not available from this repository. (Request a copy)Abstract
Using a global symbol calculus for pseudodifferential operators on tori, we build a canonical trace on classical pseudodifferential operators on noncommutative tori in terms of a canonical discrete sum on the underlying toroidal symbols. We characterise the canonical trace on operators on the noncommutative torus as well as its underlying canonical discrete sum on symbols of fixed (resp. any) noninteger order. On the grounds of this uniqueness result, we prove that in the commutative setup, this canonical trace on the noncommutative torus reduces to Kontsevich and Vishik's canonical trace which is thereby identified with a discrete sum. A similar characterisation for the noncommutative residue on noncommutative tori as the unique trace which vanishes on trace-class operators generalises Fathizadeh and Wong's characterisation in so far as it includes the case of operators of fixed integer order. By means of the canonical trace, we derive defect formulae for regularized traces. The conformal invariance of the zeta-function at zero of the Laplacian on the noncommutative torus is then a straightforward consequence.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PERIODIC PSEUDODIFFERENTIAL-OPERATORS; C-STAR-ALGEBRAS; CROSSED-PRODUCTS; CALCULUS; SYMBOLS; SPACES; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Mar 2019 08:06 |
| Last Modified: | 15 Mar 2019 08:06 |
| URI: | https://pred.uni-regensburg.de/id/eprint/2520 |
Actions (login required)
 |
View Item |
