Overview

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.

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9780198535706

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