An Introduction to Spectral Theory

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R.T. Edwards, Inc., 2005 - Science - 192 pages
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A brief and accessible introduction to the spectral theory of linear second order elliptic differential operators. By introducing vital topics of abstract functional analysis where necessary, and using clear and simple proofs, the book develops an elegant presentation of the theory while integrating applications of basic real world problems involving the Laplacian. Suitable for use as a self-contained introduction for beginners or as a one-semester student text; contains some 25 examples and 60 exercises, most with detailed hints.
 

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Contents

Compact selfadjoint operators
25
Some examples and applications
53
Integral representation
75
Spectral decomposition of the Laplaciaii
101
Further spectral properties
125
Eigenvalues of the Laplacian
149
Some applications to hydrodynamics
163
Bibliography
191
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About the author (2005)

Los Andes University

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