Local and global symbols on compact Lie groups

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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 languageEnglish
Pages (from-to)1-37
Number of pages37
JournalJournal of Pseudo-Differential Operators and Applications
Early online date22 May 2019
DOIs
Publication 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

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