Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results
In 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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210787 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results. Raphaël Ponge. SIGMA 16 (2020), 061, 31 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862640059503607808 |
|---|---|
| author | Ponge, Raphaël |
| author_facet | Ponge, Raphaël |
| citation_txt | Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results. Raphaël Ponge. SIGMA 16 (2020), 061, 31 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In 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.
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| first_indexed | 2026-03-15T05:48:24Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210787 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T05:48:24Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ponge, Raphaël 2025-12-17T14:39:53Z 2020 Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results. Raphaël Ponge. SIGMA 16 (2020), 061, 31 pages 1815-0659 2020 Mathematics Subject Classification: 58J42; 58B34; 58J40 arXiv:1911.12164 https://nasplib.isofts.kiev.ua/handle/123456789/210787 https://doi.org/10.3842/SIGMA.2020.061 In 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. The 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results Article published earlier |
| spellingShingle | Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results Ponge, Raphaël |
| title | Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results |
| title_full | Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results |
| title_fullStr | Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results |
| title_full_unstemmed | Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results |
| title_short | Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results |
| title_sort | noncommutative residue and canonical trace on noncommutative tori. uniqueness results |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210787 |
| work_keys_str_mv | AT pongeraphael noncommutativeresidueandcanonicaltraceonnoncommutativetoriuniquenessresults |