Quantization on Groups and Garding inequality

2023/07/28 by Lino Benedetto, Clotilde Fermanian Kammerer, Benedetto, Lino +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2307.15352

openalex publication_date 2023/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce Wick's quantization on groups and discuss its links with Kohn-Nirenberg's. By quantization, we mean an operation that associates an operator to a symbol. The notion of symbols for both quantizations is based on representation theory via the group Fourier transform and the Plancherel theorem. As an application, we give a simple proof of Garding inequalities for three globally symbolic pseudo-differential calculi on groups.

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