Pseudo-differential operators with nonlinear quantizing functions

In this paper we develop the calculus of pseudo-differential operators corresponding to the quantizations of the form Au(x) = Rn Rn ei(x- y)center dot.s( x + t(y - x),.)u(y) dy d., where t : Rn. Rn is a general function. In particular, for the linear choices t(x) = 0, t(x) = x and t(x) = x/2 this covers the well-known Kohn-Nirenberg, anti-Kohn-Nirenberg and Weyl quantizations, respectively. Quantizations of such type appear naturally in the analysis on nilpotent Lie groups for polynomial functions t and here we investigate the corresponding calculus in the model case of Rn. We also give examples of nonlinear t appearing on the polarized and non-polarized Heisenberg groups.

Jaar van publicatie:2020

Toegankelijkheid:Open