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Inequalities

Selecta of Elliott H. Lieb

  • Michael Loss
  • Mary Beth Ruskai

Table of contents

  1. Front Matter
    Pages I-IX
  2. Commentaries

    1. Michael Loss, Mary Beth Ruskai
      Pages 1-29
  3. Inequalities Related to Statistical Mechanics and Condensed Matter

    1. Front Matter
      Pages 31-31
    2. Elliott Lieb, Daniel Mattis
      Pages 43-45
    3. Huzihiro Araki, Elliott H. Lieb
      Pages 47-57
    4. Elliott H. Lieb, Mary Beth Ruskai
      Pages 59-61
    5. Elliott H. Lieb, Mary Beth Ruskai
      Pages 63-66
    6. Elliott H. Lieb
      Pages 91-94
    7. Elliott H. Lieb, Michael Aizenman
      Pages 95-98
  4. Matrix Inequalities and Combinatorics

    1. Front Matter
      Pages 99-99
    2. Elliott H. Lieb
      Pages 101-108
    3. Elliott H. Lieb, Mary Beth Ruskai
      Pages 135-139
    4. Michael Aizenman, E. Brian Davies, Elliott H. Lieb
      Pages 147-149
    5. Keith Ball, Eric A. Carlen, Elliott H. Lieb
      Pages 171-190
  5. Inequalities Related to the Stability of Matter

  6. Coherent States

    1. Front Matter
      Pages 343-343
    2. Elliott H. Lieb
      Pages 345-358
    3. Elliott H. Lieb
      Pages 359-365
    4. Elliott H. Lieb, Jan Philip Solovej
      Pages 367-376
  7. Brunn-Minkowski Inequality and Rearrangements

  8. General Analysis

About this book

Introduction

Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H. Lieb has discovered a host of inequalities that are enormously useful in mathematics as well as in physics. His results are collected in this book which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics.

Keywords

Coherent States Condensed Matter Harmonic Map Inequalities Potential STATISTICA Stability of Matter Statistical Mechanics distribution functional analysis linear optimization quantum physics

Editors and affiliations

  • Michael Loss
    • 1
  • Mary Beth Ruskai
    • 2
  1. 1.School of MathematicsGeorgia TechAtlantaUSA
  2. 2.Department of MathematicsUniversity of Massachusetts LowellLowellUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-55925-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-62758-3
  • Online ISBN 978-3-642-55925-9
  • Buy this book on publisher's site