Differential structure on the dual of a compact Lie group

Véronique Fischer

doi:10.1016/j.jfa.2020.108555

Differential structure on the dual of a compact Lie group

Véronique Fischer

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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 language	English
Article number	108555
Journal	Journal of Functional Analysis
Volume	279
Issue number	3
Early online date	10 Apr 2020
DOIs	https://doi.org/10.1016/j.jfa.2020.108555
Publication status	Published - 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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10.1016/j.jfa.2020.108555

DiffStructure.PDFAccepted author manuscript, 1.03 MBLicence: CC BY-NC-ND

https://arxiv.org/pdf/1610.06348.pdfLicence: CC BY

Cite this

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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 H{\"o}rmander, Mihlin and Marcinkiewicz types together with the sharpness in the Sobolev exponent for the result of H{\"o}rmander type.",

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AB - 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.

KW - Differential calculus over a non-commutative algebra

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KW - Homogeneous Sobolev spaces

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Differential structure on the dual of a compact Lie group

Abstract

Keywords

ASJC Scopus subject areas

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