Titlebook: Quantization on Nilpotent Lie Groups; Veronique Fischer,Michael Ruzhansky Book‘‘‘‘‘‘‘‘ 2016 The Editor(s) (if applicable) and the Author(s

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Rockland operators and Sobolev spaces,Laplacians to the non-stratified but still homogeneous (graded) setting. The terminology comes from a property conjectured by Rockland and eventually proved by Helffer and Nourrigat in [HN79], see Section 4.1.3.

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Quantization on graded Lie groups, their fractional powers and their associated Sobolev spaces studied in Chapter 4. As we have pointed out in the introduction, the graded Lie groups then become the natural setting for such analysis in the context of general nilpotent Lie groups.

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0743-1643 nd of homogeneous operators on such groups.Features a consis.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 topi

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Quantization on compact Lie groups, fact that the unitary irreducible representations of compact Lie groups are all finite dimensional. Here, in order to motivate the developments on nilpotent groups, which is the main subject of the present monograph, we briefly review key elements of this theory referring to [RT10a] or to other sources for proofs and further details.

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Book‘‘‘‘‘‘‘‘ 2016e 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..

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Preliminaries on Lie groups,t proofs referring the reader for more details to excellent sources where this material is treated from different points of view; for example, the monographs by Chevalley [Che99], Fegan [Feg91], Nomizu [Nom56], Pontryagin [Pon66], to mention only a few.