Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results

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dc.contributor.authorPonge, Raphaël
dc.date.accessioned2025-12-17T14:39:53Z
dc.date.issued2020
dc.description.abstractIn this paper, we establish uniqueness theorems for the noncommutative residue and the canonical trace on pseudodifferential operators on noncommutative tori of arbitrary dimension. The former is the unique trace up to a constant multiple of integer order pseudodifferential operators. The latter is the unique trace up to a constant multiple on non-integer order pseudodifferential operators. This improves previous uniqueness results by Fathizadeh-Khalkhali, Fathizadeh-Wong, and Lévy-Neira-Paycha.
dc.description.sponsorshipThe research for this article was partially supported by the NSFC under Grant No. 11971328 (China). The author thanks Sylvie Paycha for discussions related to the subject matter of the paper. He also thanks the University of Montreal (Canada) for its hospitality during the writing of the paper.
dc.identifier.citationNoncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results. Raphaël Ponge. SIGMA 16 (2020), 061, 31 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2020.061
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 58J42; 58B34; 58J40
dc.identifier.otherarXiv:1911.12164
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/210787
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleNoncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2020, том 16, випуск за цей рік