Continuous Linear Representations (eBook)

Z. Magyar (Autor)

eBook Download: PDF

1992 | 1. Auflage
300 Seiten
Elsevier Science (Verlag)
978-0-08-087279-7 (ISBN)

Infos

This monograph gives access to the theory of continuous linear representations of general real Lie groups to readers who are already familiar with the rudiments of functional analysis and Lie groups. The first half of the book is centered around the relation between a continuous linear representation (of a Lie group over a Banach space or even a more general space) and its tangent, the latter is a Lie algebra representation in a sense. Starting with the Hille-Yosida theory, quite recent results are reached. The second half is more standard unitary theory with applications concerning the Galilean and Poincaré, groups. Appendices help readers with diverse backgrounds to find the precise descriptions of the concepts needed from earlier literature.
Each chapter includes exercises.

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This monograph gives access to the theory of continuous linear representations of general real Lie groups to readers who are already familiar with the rudiments of functional analysis and Lie groups. The first half of the book is centered around the relation between a continuous linear representation (of a Lie group over a Banach space or even a more general space) and its tangent; the latter is a Lie algebra representation in a sense. Starting with the Hille-Yosida theory, quite recent results are reached. The second half is more standard unitary theory with applications concerning the Galilean and Poincare groups. Appendices help readers with diverse backgrounds to find the precise descriptions of the concepts needed from earlier literature.Each chapter includes exercises.

Inhalt

Cover 1
Copyright Page 5
Preface 6
TOC$Contents 8
Introduction 10
CH$Chapter 1. The Hille–Yosida Theory 12
CH$Chapter 2. Convolution and Regularization 34
CH$Chapter 3. Smooth Vectors 48
CH$Chapter 4. Analytic Mollifying 82
CH$Chapter 5. The Integrability Problem 100
CH$Chapter 6. Compact Groups 122
CH$Chapter 7. Commutative Groups 148
CH$Chapter 8. Induced Representations 164
CH$Chapter 9. Projective Representations 180
CH$Chapter 10. The Galilean and Poincare Groups 198
Appendix 215
A. Topology 216
B. Measure and Integration 220
C. Functional Analysis 228
D. Analytic Mappings 244
E. Manifolds, Distributions, Differential Operators 250
F. Locally Compact Groups, Lie Groups 278
References 292
Index of Notation 300
IDX$Index 302

Produkt-Details

• Erscheint lt. Verlag: 30.1.1992
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• ISBN-10: 0-08-087279-4 / 0080872794
• ISBN-13: 978-0-08-087279-7 / 9780080872797