Linear Operators in Hilbert Spaces

  • Joachim Weidmann

Part of the Graduate Texts in Mathematics book series (GTM, volume 68)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Joachim Weidmann
    Pages 15-28
  3. Joachim Weidmann
    Pages 29-49
  4. Joachim Weidmann
    Pages 50-87
  5. Joachim Weidmann
    Pages 88-128
  6. Joachim Weidmann
    Pages 129-165
  7. Joachim Weidmann
    Pages 229-268
  8. Joachim Weidmann
    Pages 269-288
  9. Joachim Weidmann
    Pages 289-336
  10. Joachim Weidmann
    Pages 337-361
  11. Back Matter
    Pages 362-402

About this book


This English edition is almost identical to the German original Lineare Operatoren in Hilbertriiumen, published by B. G. Teubner, Stuttgart in 1976. A few proofs have been simplified, some additional exercises have been included, and a small number of new results has been added (e.g., Theorem 11.11 and Theorem 11.23). In addition a great number of minor errors has been corrected. Frankfurt, January 1980 J. Weidmann vii Preface to the German edition The purpose of this book is to give an introduction to the theory of linear operators on Hilbert spaces and then to proceed to the interesting applica­ tions of differential operators to mathematical physics. Besides the usual introductory courses common to both mathematicians and physicists, only a fundamental knowledge of complex analysis and of ordinary differential equations is assumed. The most important results of Lebesgue integration theory, to the extent that they are used in this book, are compiled with complete proofs in Appendix A. I hope therefore that students from the fourth semester on will be able to read this book without major difficulty. However, it might also be of some interest and use to the teaching and research mathematician or physicist, since among other things it makes easily accessible several new results of the spectral theory of differential operators.


Hilbert space Hilbertscher Raum Koordinatentransformation Lebesgue integration Operators complex analysis convergence differential equation integral integration linearer Operator operator ordinary differential equation schrödinger operator spectral theorem

Authors and affiliations

  • Joachim Weidmann
    • 1
  1. 1.Institut für Angewandte MathematikMathematisches Seminar der Johann-Wolfgang-Goethe-Universität6 Frankfurt a. M.Federal Republic of Germany

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York Inc. 1980
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6029-5
  • Online ISBN 978-1-4612-6027-1
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • Buy this book on publisher's site