This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups.

The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.

First Open Access book in the Birkhäuser program Contains a detailed and easy-to-follow exposition of nilpotent and homogeneous Lie groups and of homogeneous operators on such groups Features a consistent development of the theory of Sobolev spaces on graded Lie groups Gives a detailed development of the pseudo-differential analysis on graded Lie groups The developed theory is thoroughly illustrated in the case of the Heisenberg group providing new links with various topics of analysis in this setting

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