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Lecture Notes in Mathematics

Spectral Theory of Ordinary Differential Operators

Authors: Weidmann, Joachim

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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.

Table of contents (22 chapters)

Table of contents (22 chapters)

Buy this book

eBook $34.99
price for USA in USD
  • ISBN 978-3-540-47912-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $46.00
price for USA in USD
  • ISBN 978-3-540-17902-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Spectral Theory of Ordinary Differential Operators
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1258
Copyright
1987
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-47912-3
DOI
10.1007/BFb0077960
Softcover ISBN
978-3-540-17902-3
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 304
Topics