Advertisement

Probabilities on the Heisenberg Group

Limit Theorems and Brownian Motion

  • Authors
  • Daniel¬†Neuenschwander

Part of the Lecture Notes in Mathematics book series (LNM, volume 1630)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Daniel Neuenschwander
    Pages 1-6
  3. Daniel Neuenschwander
    Pages 29-84
  4. Daniel Neuenschwander
    Pages 85-123
  5. Back Matter
    Pages 125-139

About this book

Introduction

The Heisenberg group comes from quantum mechanics and is the simplest non-commutative Lie group. While it belongs to the class of simply connected nilpotent Lie groups, it turns out that its special structure yields many results which (up to now) have not carried over to this larger class. This book is a survey of probabilistic results on the Heisenberg group. The emphasis lies on limit theorems and their relation to Brownian motion. Besides classical probability tools, non-commutative Fourier analysis and functional analysis (operator semigroups) comes in. The book is intended for probabilists and analysts interested in Lie groups, but given the many applications of the Heisenberg group, it will also be useful for theoretical phycisists specialized in quantum mechanics and for engineers.

Keywords

Brownian motion Probability theory functional analysis linear optimization mechanics operator quantum mechanics

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0094029
  • Copyright Information Springer-Verlag Berlin Heidelberg 1996
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-61453-1
  • Online ISBN 978-3-540-68590-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site