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  • © 1987

Spectral Theory of Ordinary Differential Operators

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

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Table of contents (22 chapters)

  1. Front Matter

    Pages I-VI
  2. Introduction

    • Joachim Weidmann
    Pages 1-6
  3. Fundamental properties and general assumptions

    • Joachim Weidmann
    Pages 23-35
  4. The minimal operator and the maximal operator

    • Joachim Weidmann
    Pages 41-51
  5. Limit point-limit circle criteria

    • Joachim Weidmann
    Pages 88-103
  6. The resolvents of self-adjoint extensions of T0

    • Joachim Weidmann
    Pages 110-125
  7. Computation of the spectral matrix ϱ

    • Joachim Weidmann
    Pages 140-149
  8. L2-solutions and essential spectrum

    • Joachim Weidmann
    Pages 162-171
  9. Differential operators with periodic coefficients

    • Joachim Weidmann
    Pages 172-190

About this book

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

  • Book Title: Spectral Theory of Ordinary Differential Operators

  • Authors: Joachim Weidmann

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0077960

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • Softcover ISBN: 978-3-540-17902-3Published: 06 May 1987

  • eBook ISBN: 978-3-540-47912-3Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 304

  • Topics: Analysis

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions