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In this mini-course we will introduce a pseudo-differential calculus on graded nilpotent Lie groups recently developed in collaboration with D. Rottensteiner and M. Ruzhansky. This calculus represents the Weyl calculus on the Heisenberg group and the right candidate Weyl calculus in the general graded group setting. This Weyl quantization, along with the corresponding calculus, will be suitably identified within the family of the so-called τ -quantizations.
Part of the Spring School
'Modern Aspects of Analysis on Lie Groups'
https://jaeh.cc/SS2024/index.htm