Spectral Theory of Ordinary Differential Operators

  • Authors
  • Joachim Weidmann

Part of the Lecture Notes in Mathematics book series (LNM, volume 1258)

Table of contents

  1. Front Matter
    Pages I-VI
  2. Joachim Weidmann
    Pages 1-6
  3. Joachim Weidmann
    Pages 23-35
  4. Joachim Weidmann
    Pages 41-51
  5. Joachim Weidmann
    Pages 88-103
  6. Joachim Weidmann
    Pages 110-125
  7. Joachim Weidmann
    Pages 140-149
  8. Joachim Weidmann
    Pages 162-171
  9. Joachim Weidmann
    Pages 172-190

About this book

Introduction

These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differential expressions of arbitrary order n operating on -valued functions existence and construction of self-adjoint realizations via boundary conditions, determination and study of general properties of the resolvent, spectral representation and spectral resolution. Special attention is paid to the question of separated boundary conditions, spectral multiplicity and absolutely continuous spectrum. For the case nm=2 (Sturm-Liouville operators and Dirac systems) the classical theory of Weyl-Titchmarch is included. Oscillation theory for Sturm-Liouville operators and Dirac systems is developed and applied to the study of the essential and absolutely continuous spectrum. The results are illustrated by the explicit solution of a number of particular problems including the spectral theory one partical Schrödinger and Dirac operators with spherically symmetric potentials. The methods of proof are functionally analytic wherever possible.

Keywords

Dirac operator Hilbert space differential equation maximum minimum

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0077960
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-17902-3
  • Online ISBN 978-3-540-47912-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book