Spectral theory and differential operators
著者
書誌事項
Spectral theory and differential operators
（Oxford mathematical monographs）
Clarendon Press, 1989, c1987
- : pbk
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注記
Bibliography: p. [556]-566
Includes indexes
内容説明・目次
内容説明
This book contains an up-to-date account of those parts of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. The main themes are essential spectra, measures of non-compactness, entropy numbers, approximation numbers, eigenvalues and their interrelationships. The abstract theory is illustrated by results for embedding maps between Sobolev spaces, and strong emphasis is placed on application to boundary-value problems for general second-order linear elliptic equations in an arbitrary domain in Rn. Much work has been done in these areas in recent years, and the book provides a survey of this. Although the prime audience is seen as graduate mathematicians, it is hoped that other scientists will also find this book useful.
目次
- Linear operations in Banach spaces
- Entropy numbers, s-numbers, and eigenvalues
- Unbounded linear operators
- Sesquilinear forms in Hilbert spaces
- Sobolev spaces
- Generalized Dirichlet and Neumann boundary-value problems
- Second-order differential operators on arbitrary open sets
- Capacity and compactness criteria
- Essential spectra
- Essential spectra of general second-order differential operators
- Global and asymptotic estimates for the eigen-values of - + q when q is real.
- Estimates for the singular values of - + q when 1 is complete
- Bibliography
- Notation index
- Subject index
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