Quantization on Nilpotent Lie Groups / by Veronique Fischer, Michael Ruzhansky.

Format:

Book

Author/Creator:

Fischer, Veronique, Author.

Ruzhansky, M. (Michael), Author.

Series:

Progress in Mathematics, 0743-1643 ; 314

Language:

English

Subjects (All):

Topological groups.

Lie groups.

Harmonic analysis.

Functional analysis.

Mathematical physics.

Topological Groups, Lie Groups.

Abstract Harmonic Analysis.

Functional Analysis.

Mathematical Physics.

Local Subjects:

Topological Groups, Lie Groups.

Abstract Harmonic Analysis.

Functional Analysis.

Mathematical Physics.

Physical Description:

1 online resource (XIII, 557 p. 1 illus. in color.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.

Language Note:

English

Summary:

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.

Contents:

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-29558-6

OCLC:

945948187