ISBN : 9780198812050
This book is an updated version of the classic monograph Spectral Theory and Differential Operators, published by OUP in 1987. The original book was a cutting edge account of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.
1 Linear operators in Banach spaces
2 Entropy numbers, s-numbers, and eigenvalues
3 Unbounded linear operators
4 Sesqilinear forms in Hilbert spaces
5 Sobolve spaces
6 Generalized Dirichlet and Neumann boundary-value problems
7 Second-order differantial operators on arbitary open sets
8 Capacity and compactness criteria
9 Essential spectra
10 Essential spectra of general second-order differential operators
11 Global and asymptotic estimates for the eigenvalues
12 Estimates of the singular values
Bibliography