Quantization on Nilpotent Lie Groups

Description

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. Front Matter....Pages i-xxviii Preliminaries on Lie groups....Pages 15-56 Quantization on compact Lie groups....Pages 57-90 Homogeneous Lie groups....Pages 91-170 Rockland operators and Sobolev spaces....Pages 171-269 Quantization on graded Lie groups....Pages 271-426 Pseudo-differential operators on the Heisenberg group....Pages 427-489 Back Matter....Pages 491-557