Spectral Theory and Differential Operators

Spectral Theory and Differential Operators

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Cambridge University Press

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Spectral Theory and Differential Operators

In this book, Davies introduces the reader to the theory of partial differential operators, up to the spectral theorem for bounded linear operators on Banach spaces. He also describes the theory of Fourier transforms and distributions as far as is needed to analyze the spectrum of any constant coefficient partial differential operator. He also presents a completely new proof of the spectral theorem for unbounded self-adjoint operators and demonstrates its application to a variety of second order elliptic differential operators. Finally, the book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques. Illustrated with many examples, it is well-suited to graduate-level work.

Product Details

ISBN-13: 9780521587105
Publisher: Cambridge University Press
Publication date: 02/28/2003
Series: Cambridge Studies in Advanced Mathematics Series , #42
Edition description: New Edition
Pages: 196
Product dimensions: 5.98(w) x 8.98(h) x 0.43(d)

Table of Contents

1. The fundamental ideas; 2. The spectral theorem; 3. Translation invariant operators; 4. The variation methods; 5. Further spectral results; 6. Dirichlet boundary conditions; 7. Neumann boundary conditions; 8. Schrödinger operators.

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