Edmunds D., Evans D. Spectral Theory and Differential Operators

2nd. ed. - Oxford: Oxford University Press, 2018. - 609 p. - (Oxford Mathematical Monographs). - ISBN: 0198812051.This book is an updated version of the classic 1987 monograph "Spectral Theory and Differential Operators". 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. It is accessible to a graduate student as well as meeting the needs of seasoned researchers in mathematics and mathematical physics. 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.Basic Notation
Linear Operators 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 Eigenvalues of − + q when q Is Real.
Estimates for the Singular Values of − + q when q is Complex.Author Index.
Notation Index.
Subject Index.True PDF