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.
Funding Statement
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.
Citation
Lino BENEDETTO. Clotilde FERMANIAN KAMMERER. Véronique FISCHER. "Wick quantization on groups and application to Gårding inequalities." J. Math. Soc. Japan Advance Publication 1 - 36, November, 2024. https://doi.org/10.2969/jmsj/92149214
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