Hilbert Spaces: A Brief Historical Introduction
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.
KeywordsHilbert Space Linear Operator Weak Topology Essential Spectrum Finite Dimensional Space
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