Chapter 5. Hilbert–Schmidt Theory of Symmetric Kernel

  1. Dr. Michio Masujima

Published Online: 27 NOV 2009

DOI: 10.1002/9783527627745.ch5

Applied Mathematical Methods in Theoretical Physics, Second Edition

Applied Mathematical Methods in Theoretical Physics, Second Edition

How to Cite

Masujima, M. (2009) Hilbert–Schmidt Theory of Symmetric Kernel, in Applied Mathematical Methods in Theoretical Physics, Second Edition, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527627745.ch5

Author Information

  1. Tokyo, Japan

Publication History

  1. Published Online: 27 NOV 2009
  2. Published Print: 19 AUG 2009

ISBN Information

Print ISBN: 9783527409365

Online ISBN: 9783527627745

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Keywords:

  • theoretical physics;
  • applied mathematical methods;
  • Hilbert–Schmidt theory;
  • symmetric kernel;
  • Sturm–Liouville system

Summary

This chapter contains sections titled:

  • Real and Symmetric Matrix

  • Real and Symmetric Kernel

  • Bounds on the Eigenvalues

  • Rayleigh Quotient

  • Completeness of Sturm–Liouville Eigenfunctions

  • Generalization of Hilbert–Schmidt Theory

  • Generalization of the Sturm–Liouville System

  • Problems for Chapter 5