Pseudodifferential Operators on Noncommutative Tori: a Survey
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914875163279360 |
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| author | Jiménez, Carolina Neira |
| author_facet | Jiménez, Carolina Neira |
| contents | This article presents a survey of recent developments on pseudodifferential operators on noncommutative tori. We describe currently available constructions of those operators: by means of a $C^*$--dynamical system, by using an analogue of the Fourier series representation of a function in the (commutative) torus $C^\infty(\mathbb{T}^n)$, as Rieffel deformations of the standard pseudodifferential operators on $C^\infty(\mathbb{T}^n)$, and in association to certain spectral triples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03584 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Pseudodifferential Operators on Noncommutative Tori: a Survey Jiménez, Carolina Neira Operator Algebras 58B34, 53D55, 47G30 This article presents a survey of recent developments on pseudodifferential operators on noncommutative tori. We describe currently available constructions of those operators: by means of a $C^*$--dynamical system, by using an analogue of the Fourier series representation of a function in the (commutative) torus $C^\infty(\mathbb{T}^n)$, as Rieffel deformations of the standard pseudodifferential operators on $C^\infty(\mathbb{T}^n)$, and in association to certain spectral triples. |
| title | Pseudodifferential Operators on Noncommutative Tori: a Survey |
| topic | Operator Algebras 58B34, 53D55, 47G30 |
| url | https://arxiv.org/abs/2303.03584 |