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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.

Algebra --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Mathematics. --- Topological groups. --- Lie groups. --- Harmonic analysis. --- Functional analysis. --- Mathematical physics. --- Topological Groups, Lie Groups. --- Abstract Harmonic Analysis. --- Functional Analysis. --- Mathematical Physics. --- Physical mathematics --- Physics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Mathematical analysis --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Math --- Science --- Topological Groups. --- Medicine. --- Public health. --- Medical research. --- Biomedicine, general. --- Public Health. --- Quality of Life Research. --- Biomedicine general --- Public Health --- Quality of Life Research --- Population Health --- EQ-5D --- Quality-of-Life --- Utilities