Pseudo-differential operators and quantization (Q2776615)

This article contains a portion of lectures presenting an introduction to the theory of pseudodifferential operators.NEWLINENEWLINENEWLINEThe article under review discusses classical and quantum mechanics, pseudodifferential operators in \(\mathbb{R}^n\), canonical transformations, and pseudodifferential operators in the general theory of partial differential equations. The presentation of each topic is brief and clear. It motivates very well the introduction of appropriate classes of pseudodifferential operators in a quantization, that is to say in a way of making the transition from classical mechanics to quantum mechanics. The last section illustrates the role of pseudodifferential operators in solvability problems for linear partial differential equations. In this context, the author discusses elliptic and subelliptic operators as well as the role of a priori estimates. The author also points out at the use of techniques from quantization to prove results concerning subelliptic pseudodifferential operators.NEWLINENEWLINENEWLINEThe article does not include proofs for most of the results, but it lists appropriate references.NEWLINENEWLINEFor the entire collection see [Zbl 0977.00018].