Coherent states and evolution equations. (English) Zbl 0865.35153

Qi, Min-You (ed.) et al., General theory of partial differential equations and microlocal analysis. Proceedings of a workshop, ICTP, Trieste, Italy, September 4–15, 1995. Harlow: Longman. Pitman Res. Notes Math. Ser. 349, 123-154 (1996).
Given a Hamiltonian \(a(x,\xi)\) on the phase space \(\mathbb{R}^n\times\mathbb{R}^n\), one can associate linearly an operator \(A\) by various quantization formulas (standard quantization, Weyl quantization, Wick quantization). After an exposition of the Weyl quantization, the author describes the Wick-Berezin quantization. He then applies the Wick-Berezin quantization to a new proof of Treves’ theorem on subellipticity for differential operators of principal type.
For the entire collection see [Zbl 0845.00043].


35S05 Pseudodifferential operators as generalizations of partial differential operators
65H10 Numerical computation of solutions to systems of equations
81S10 Geometry and quantization, symplectic methods