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Birkhäuser

A Birman-Schwinger Principle in Galactic Dynamics

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  • © 2021

Overview

Authors:
  1. Markus Kunze

    1. Mathematisches Institut, Universität zu Köln, Cologne, Germany

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  • Connects a mathematical principle used in quantum mechanics to the study of steady state solutions in galactic dynamics
  • Presents a novel result in great detail
  • Includes appendices that cover necessary background material

Part of the book series: Progress in Mathematical Physics (PMP, volume 77)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Markus Kunze
    Pages 1-21

  3. The Antonov Stability Estimate

    • Markus Kunze
    Pages 23-27

  4. On the Period Function \(T_1\)

    • Markus Kunze
    Pages 29-52

  5. A Birman-Schwinger Type Operator

    • Markus Kunze
    Pages 53-88

  6. Relation to the Guo-Lin Operator

    • Markus Kunze
    Pages 89-92

  7. Invariances

    • Markus Kunze
    Pages 93-99

  8. Back Matter

    Pages 101-206
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Keywords

About this book

This monograph develops an innovative approach that utilizes the Birman-Schwinger principle from quantum mechanics to investigate stability properties of steady state solutions in galactic dynamics.  The opening chapters lay the framework for the main result through detailed treatments of nonrelativistic galactic dynamics and the Vlasov-Poisson system, the Antonov stability estimate, and the period function $T_1$.  Then, as the main application, the Birman-Schwinger type principle is used to characterize in which cases the “best constant” in the Antonov stability estimate is attained.  The final two chapters consider the relation to the Guo-Lin operator and invariance properties for the Vlasov-Poisson system, respectively.  Several appendices are also included that cover necessary background material, such as spherically symmetric models, action-angle variables, relevant function spaces and operators, and some aspects of Kato-Rellich perturbation theory.  


A Birman-Schwinger Principle in Galactic Dynamics will be of interest to researchers in galactic dynamics, kinetic theory, and various aspects of quantum mechanics, as well as those in related areas of mathematical physics and applied mathematics.

Reviews

“The book is written for specialists in galactic dynamics and for mathematical physicists attracted by gravity. … The reward comes in understanding many aspects of the Vlasov-Poisson equation in a rigorous mathematically exact way.” (Marek Nowakowski, Mathematical Reviews, October, 2022)

Authors and Affiliations

  • Mathematisches Institut, Universität zu Köln, Cologne, Germany

    Markus Kunze

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