Non-commutative Analysis
Nonfiction, Science & Nature, Mathematics, Functional Analysis, Mathematical Analysis
| Author: | Palle Jorgensen, Feng Tian | ISBN: | 9789813202146 |
| Publisher: | World Scientific Publishing Company | Publication: | January 24, 2017 |
| Imprint: | WSPC | Language: | English |
| Author: | Palle Jorgensen, Feng Tian |
| ISBN: | 9789813202146 |
| Publisher: | World Scientific Publishing Company |
| Publication: | January 24, 2017 |
| Imprint: | WSPC |
| Language: | English |
The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret "non-commutative analysis" broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.)
A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras.
The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.
Contents:
-
Foreword
-
Preface
-
Acknowledgments
-
Abbreviations, Notation, Some Core Theorems
-
Introduction and Motivation:
- Subjects and User's Guide
-
Topics from Functional Analysis and Operators in Hilbert Space: A Selection:
- Elementary Facts
- Unbounded Operators in Hilbert Space
- Spectral Theory
-
Applications:
- GNS and Representations
- Completely Positive Maps
- Brownian Motion
- Lie Groups, and Their Unitary Representations
- The Kadison-Singer Problem
-
Extension of Operators:
- Selfadjoint Extensions
- Unbounded Graph-Laplacians
- Reproducing Kernel Hilbert Space
-
Appendices:
- An Overview of Functional Analysis Books (Cast of Characters)
- Terminology from Neighboring Areas
- Often Cited
- Prizes and Fame
- List of Exercises
- Definitions of Frequently Occurring Terms
- List of Figures
-
List of Tables
-
Bibliography
-
Index
Readership: Undergraduates, graduate students and researchers in operator theory, functional analysis, mathematical physics, complex analysis, stochastic analysis, quantum mechanics.
The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret "non-commutative analysis" broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.)
A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras.
The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.
Contents:
-
Foreword
-
Preface
-
Acknowledgments
-
Abbreviations, Notation, Some Core Theorems
-
Introduction and Motivation:
- Subjects and User's Guide
-
Topics from Functional Analysis and Operators in Hilbert Space: A Selection:
- Elementary Facts
- Unbounded Operators in Hilbert Space
- Spectral Theory
-
Applications:
- GNS and Representations
- Completely Positive Maps
- Brownian Motion
- Lie Groups, and Their Unitary Representations
- The Kadison-Singer Problem
-
Extension of Operators:
- Selfadjoint Extensions
- Unbounded Graph-Laplacians
- Reproducing Kernel Hilbert Space
-
Appendices:
- An Overview of Functional Analysis Books (Cast of Characters)
- Terminology from Neighboring Areas
- Often Cited
- Prizes and Fame
- List of Exercises
- Definitions of Frequently Occurring Terms
- List of Figures
-
List of Tables
-
Bibliography
-
Index
Readership: Undergraduates, graduate students and researchers in operator theory, functional analysis, mathematical physics, complex analysis, stochastic analysis, quantum mechanics.
