Local and global symbols on compact Lie groups

Research output: Contribution to journalArticle

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.

LanguageEnglish
Pages1-37
Number of pages37
JournalJournal of Pseudo-Differential Operators and Applications
Early online date22 May 2019
DOIs
StatusE-pub ahead of print - 22 May 2019

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

Cite this

Local and global symbols on compact Lie groups. / Fischer, Véronique.

In: Journal of Pseudo-Differential Operators and Applications, 22.05.2019, p. 1-37.

Research output: Contribution to journalArticle

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