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 prove Gårding inequalities for three global symbolic pseudodifferential calculi on groups.
| Original language | English |
|---|---|
| Pages (from-to) | 797-832 |
| Number of pages | 36 |
| Journal | Journal of the Mathematical Society of Japan |
| Volume | 77 |
| Issue number | 3 |
| Early online date | 12 Nov 2024 |
| DOIs | |
| Publication status | Published - 31 Jul 2025 |
Funding
2020 Mathematics Subject Classification. Primary 43A80. Key Words and Phrases. abstract harmonic analysis, pseudodifferential calculus on compact and nilpotent Lie groups, Gårding inequality. The first and second authors benefit from the support of the Région Pays de la Loire via the Connect Talent Project HiFrAn 2022 07750, and from the France 2030 program, Centre Henri Lebesgue ANR-11-LABX-0020-01. The second and third authors acknowledge the support of the Leverhulme Trust via Research Project Grant RPG 2020-037.
Keywords
- abstract harmonic analysis
- Gårding inequality
- pseudodifferential calculus on compact and nilpotent Lie groups
ASJC Scopus subject areas
- General Mathematics
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