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Quantization on Nilpotent Lie Groups [electronic resource] / by Veronique Fischer, Michael Ruzhansky.
By: Fischer, Veronique [author.].
Contributor(s): Ruzhansky, Michael [author.] | SpringerLink (Online service).
Material type:
TextSeries: Progress in Mathematics: 314Publisher: Cham : Springer International Publishing : Imprint: Birkhäuser, 2016Edition: 1st ed. 2016.Description: XIII, 557 p. 1 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319295589.Subject(s): Mathematics | Topological groups | Lie groups | Harmonic analysis | Functional analysis | Mathematical physics | Mathematics | Topological Groups, Lie Groups | Abstract Harmonic Analysis | Functional Analysis | Mathematical PhysicsAdditional physical formats: Printed edition:: No titleDDC classification: 512.55 | 512.482 Online resources: Click here to access online
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Springer eBooksSummary: 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.
Preface -- Introduction -- Notation and conventions -- 1 Preliminaries on Lie groups -- 2 Quantization on compact Lie groups -- 3 Homogeneous Lie groups -- 4 Rockland operators and Sobolev spaces -- 5 Quantization on graded Lie groups -- 6 Pseudo-differential operators on the Heisenberg group -- A Miscellaneous -- B Group C* and von Neumann algebras -- Schrödinger representations and Weyl quantization -- Explicit symbolic calculus on the Heisenberg group -- List of quantizations -- Bibliography -- Index.
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Preface -- Introduction -- Notation and conventions -- 1 Preliminaries on Lie groups -- 2 Quantization on compact Lie groups -- 3 Homogeneous Lie groups -- 4 Rockland operators and Sobolev spaces -- 5 Quantization on graded Lie groups -- 6 Pseudo-differential operators on the Heisenberg group -- A Miscellaneous -- B Group C* and von Neumann algebras -- Schrödinger representations and Weyl quantization -- Explicit symbolic calculus on the Heisenberg group -- List of quantizations -- Bibliography -- Index.
Open Access
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.