Wick quantization on groups and application to Gårding inequalities

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.