چكيده به لاتين
Abstract: In this thesis we study the calculus of pseudo-differential operators corresponding to the quantization of the form Au(x) = ∫ Rn ∫ Rn ei(xy)(x + (y x))u(y) dy d ; where : Rn ! Rn is a general function. In particular, for the linear choices (x) = 0; (x) = x; and (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 and here we investigate the corresponding calculus in the model case of Rn. This quantizations appear in particular in the noncommutative setting. So that a class of so-called symmetric quantizations was indentified inheriting the important property for quantum physics, that the self-adjoint symbols are quantized into self-adjoint operators. We also investigate examples of nonlinear appearing on the polarised and non-polarised heisenberg groups. Keywords: Pseudo-differential operators, Quantizations, Weyl quantization, Heisenberg group
