Sharp Gårding inequality on compact Lie groups

2010/07/31 by Michael Ruzhansky, Ville Turunen · 3 citations
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Commutative property #Inequality #Lie group #Mathematical analysis #Mathematics #Pure mathematics #Simple Lie group #Spectral Theory in Mathematical Physics #math.AP #math.FA #math.RT #msc:22E30 #msc:35S05

paper · pdf · doi:10.1016/j.jfa.2011.02.014

published as J. Funct. Anal., 260 (2011), 2881-2901 · 18 pages

arxiv created 2011/02/17 · openalex publication_date 2011/02/24 · arxiv updated 2014/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper the sharp Garding inequality is established on compact Lie groups. The positivity condition is expressed in the non-commutative phase space in terms of the full symbol, which is defined using the representations of the group. Applications are given to the L² and Sobolev boundedness of pseudo-differential operators.

Citations

• Global Quantization of Pseudo-Differential Operators on Compact Lie Groups, SU(2), 3-sphere, and Homogeneous Spaces
• The Cauchy problem for differential equations with double characteristics

Cited by

• Hörmander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity
• L^p L p Fourier multipliers on compact Lie groups
• Wave equation for sums of squares on compact Lie groups
• A pseudo-differential calculus on the Heisenberg group