Non-commutative Analysis by Palle Jorgensen

Non-commutative Analysis

byPalle Jorgensen, Feng Tian

Kobo ebook | January 24, 2017

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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.

Title:Non-commutative AnalysisFormat:Kobo ebookPublished:January 24, 2017Publisher:World Scientific Publishing CompanyLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9813202149

ISBN - 13:9789813202146

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