Differential structure on the dual of a compact Lie group

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Abstract

In this paper we define difference operators and homogeneous Sobolev-type spaces on the dual of a compact Lie group. As an application and to show that this defines a relevant differential structure, we state and prove multiplier theorems of Hörmander, Mihlin and Marcinkiewicz types together with the sharpness in the Sobolev exponent for the result of Hörmander type.

Original languageEnglish
Article number108555
JournalJournal of Functional Analysis
Volume279
Issue number3
Early online date10 Apr 2020
DOIs
Publication statusPublished - 15 Aug 2020

Keywords

  • Differential calculus over a non-commutative algebra
  • Harmonic analysis on compact Lie groups
  • Homogeneous Sobolev spaces

ASJC Scopus subject areas

  • Analysis

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