Spectral theory | Wikipedia audio article
Channel: Subhajit Sahu
Date: 2018-12-27

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Spectral_theory


00:00:40 1 Mathematical background
00:03:32 2 Physical background
00:05:15 3 A definition of spectrum
00:08:34 4 Spectral theory briefly
00:16:28 5 Resolution of the identity
00:25:50 6 Resolvent operator
00:26:55 7 Operator equations
00:37:34 8 Spectral theorem and Rayleigh quotient
00:46:07 9 See also
00:55:28 10 Notes



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SUMMARY
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In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result of studies of linear algebra and the solutions of systems of linear equations and their generalizations. The theory is connected to that of analytic functions because the spectral properties of an operator are related to analytic functions of the spectral parameter.