Pseudodifferential calculus on noncommutative tori, II. Main properties
| Autor: | Raphael Ponge, Gihyun Lee, Hyunsu Ha |
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| Rok vydání: | 2019 |
| Předmět: |
Series (mathematics)
Mathematics::Operator Algebras Pseudodifferential operators General Mathematics 010102 general mathematics Mathematics - Operator Algebras Torus Mathematics::Spectral Theory medicine.disease 01 natural sciences Noncommutative geometry Mathematics::K-Theory and Homology 0103 physical sciences FOS: Mathematics Calculus medicine 58B34 58J40 010307 mathematical physics 0101 mathematics Operator Algebras (math.OA) Calculus (medicine) Mathematics |
| Zdroj: | International Journal of Mathematics. 30:1950034 |
| ISSN: | 1793-6519 0129-167X |
| Popis: | This paper is the 2nd part of a two-paper series whose aim is to give a detailed description of Connes' pseudodifferential calculus on noncommutative $n$-tori, $n\geq 2$. We make use of the tools introduced in the 1st part to deal with the main properties of pseudodifferential operators on noncommutative tori of any dimension $n\geq 2$. This includes the main results mentioned in the original notes of Connes and Baaj. We also obtain further results regarding action on Sobolev spaces, spectral theory of elliptic operators, and Schatten-class properties of pseudodifferential operators of negative order, including a trace-formula for pseudodifferential operators of order $ Comment: v.3: extended account on the trace formula, new references, 52 pages |
| Databáze: | OpenAIRE |
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