Abstract
On the torus, it is possible to assign a global symbol to a pseudo-differential operator using Fourier series. In this paper we investigate the relations between the local and global symbols for the operators in the classical Hörmander calculus and describe the principal symbols, the non-commutative residue and the canonical trace of an operator in terms of its global symbol. We also generalise these results to any compact Lie group.
Original language | English |
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Pages (from-to) | 229–265 |
Journal | Journal of Pseudo-Differential Operators and Applications |
Volume | 11 |
Early online date | 22 May 2019 |
DOIs | |
Publication status | Published - 1 Mar 2020 |
Keywords
- Analysis on the torus and on compact Lie groups
- Canonical trace
- Non-commutative residue
- Pseudo-differential operators on manifolds
ASJC Scopus subject areas
- Analysis
- Applied Mathematics