Details
| Original language | English |
|---|---|
| Title of host publication | Cyclic Cohomology at 40 |
| Subtitle of host publication | Achievements and Future Prospects |
| Editors | Alain Connes, Alain Connes, Caterina Consani, Bjørn Ian Dundas, Masoud Khalkhali, Henri Moscovici |
| Publisher | American Mathematical Society |
| Pages | 457-476 |
| Number of pages | 20 |
| ISBN (print) | 9781470469771 |
| Publication status | Published - 2023 |
| Event | Virtual Conference on Cyclic Cohomology at 40: Achievements and Future Prospects, 2021 - Virtual, Online Duration: 27 Sept 2021 → 1 Oct 2021 |
Publication series
| Name | Proceedings of Symposia in Pure Mathematics |
|---|---|
| Volume | 105 |
| ISSN (Print) | 0082-0717 |
| ISSN (electronic) | 2324-707X |
Abstract
We consider the operator algebra A on p (R n ) generated by the Shubin type pseudodifferential operators, the Heisenberg-Weyl operators and the lifts of the unitary operators on C n to metaplectic operators. With the help of an auxiliary operator in the Shubin calculus, we find trace expansions for these operators in the spirit of Grubb and Seeley. Moreover, we can define a noncommutative residue generalizing that for the Shubin pseudodifferential operators and obtain a class of localized equivariant traces on the algebra.
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Cyclic Cohomology at 40: Achievements and Future Prospects. ed. / Alain Connes; Alain Connes; Caterina Consani; Bjørn Ian Dundas; Masoud Khalkhali; Henri Moscovici. American Mathematical Society, 2023. p. 457-476 (Proceedings of Symposia in Pure Mathematics; Vol. 105).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - Trace Expansions and Equivariant Traces on an Algebra of Fourier Integral Operators on Rn
AU - Savin, Anton
AU - Schrohe, Elmar
N1 - Funding Information: The second author gratefully acknowledges the support of Deutsche Forschungsgemeinschaft through grant SCHR 319/10-1. The first author is grateful for support to the Russian Foundation for Basic Research, project Nr. 21-51-12006.
PY - 2023
Y1 - 2023
N2 - We consider the operator algebra A on p (R n ) generated by the Shubin type pseudodifferential operators, the Heisenberg-Weyl operators and the lifts of the unitary operators on C n to metaplectic operators. With the help of an auxiliary operator in the Shubin calculus, we find trace expansions for these operators in the spirit of Grubb and Seeley. Moreover, we can define a noncommutative residue generalizing that for the Shubin pseudodifferential operators and obtain a class of localized equivariant traces on the algebra.
AB - We consider the operator algebra A on p (R n ) generated by the Shubin type pseudodifferential operators, the Heisenberg-Weyl operators and the lifts of the unitary operators on C n to metaplectic operators. With the help of an auxiliary operator in the Shubin calculus, we find trace expansions for these operators in the spirit of Grubb and Seeley. Moreover, we can define a noncommutative residue generalizing that for the Shubin pseudodifferential operators and obtain a class of localized equivariant traces on the algebra.
KW - math.FA
KW - 58J40, 58J42
UR - http://www.scopus.com/inward/record.url?scp=85151071806&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2204.05363
DO - 10.48550/arXiv.2204.05363
M3 - Conference contribution
SN - 9781470469771
T3 - Proceedings of Symposia in Pure Mathematics
SP - 457
EP - 476
BT - Cyclic Cohomology at 40
A2 - Connes, Alain
A2 - Connes, Alain
A2 - Consani, Caterina
A2 - Dundas, Bjørn Ian
A2 - Khalkhali, Masoud
A2 - Moscovici, Henri
PB - American Mathematical Society
T2 - Virtual Conference on Cyclic Cohomology at 40: Achievements and Future Prospects, 2021
Y2 - 27 September 2021 through 1 October 2021
ER -