Hilbert Spaces: A Brief Historical Introduction

  • Philippe Blanchard
  • Erwin Brüning
Part of the Progress in Mathematical Physics book series (PMP, volume 26)


The eigenvalue problem in finite dimensional spaces was completely solved at the end of the 19th century. At the beginning of the 20th century the focus shifted to eigenvalue problems for certain linear partial differential operators of second order (e.g., Sturm-Liouville problems) and one realized quickly that these are eigenvalue problems in infinite dimensional spaces, which presented completely new properties and unexpected difficulties.


Hilbert Space Linear Operator Weak Topology Essential Spectrum Finite Dimensional Space 
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Philippe Blanchard
    • 1
  • Erwin Brüning
    • 2
  1. 1.Faculty of PhysicsUniversity of BielefeldBielefeldGermany
  2. 2.Department of Mathematics and Applied MathematicsUniversity of Durban—WestvilleDurbanSouth Africa

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