On Sobolev norms for Lie group representations

Heiko Gimperlein, Bernhard Krötz

Research output: Contribution to journalArticlepeer-review

Abstract

We define Sobolev norms of arbitrary real order for a Banach representation (π,E) of a Lie group, with regard to a single differential operator D=dπ(R 2+Δ). Here, Δ is a Laplace element in the universal enveloping algebra, and R>0 depends explicitly on the growth rate of the representation. In particular, we obtain a spectral gap for D on the space of smooth vectors of E. The main tool is a novel factorization of the delta distribution on a Lie group.

Original languageEnglish
Article number108882
JournalJournal of Functional Analysis
Volume280
Issue number4
Early online date1 Dec 2020
DOIs
Publication statusPublished - 15 Feb 2021

Keywords

  • Factorization of the delta-distribution
  • Representations of Lie groups
  • Sobolev norms for representations

ASJC Scopus subject areas

  • Analysis

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