Spectral Theory and Differential Operators / Edition 2

by David Edmunds, Des Evans

Overview

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.

Product Details

ISBN-13:	9780198812050
Publisher:	Oxford University Press
Publication date:	07/23/2018
Series:	Oxford Mathematical Monographs
Edition description:	2nd ed.
Pages:	610
Product dimensions:	9.30(w) x 6.30(h) x 1.30(d)

About the Author

David Edmunds, Emeritus Professor (Mathematics, Analysis and Partial Differential Equations Research Group), University of Sussex,Des Evans, Emeritus Professor of Mathematics, Cardiff University

Professor David Edmunds is Emeritus Professor of the Mathematics, Analysis and Partial Differential Equations Research Group at University of Sussex. His main research interests are functional analysis, interpolation theory, the theory of function spaces, sharp estimates of s-numbers and entropy numbers of embeddings and classical operators, and elliptic partial differential equations. He was awarded the LMS Polya prize in 1996, the Czech Academy of Sciences Bolzano prize in 1998, and was elected to a fellowship of the Learned Society of Wales in 2012.

Professor Des Evans of Emeritus Professor of Mathematics at Cardiff University. His main research interests are in the spectral theory associated with differential equations and related areas of analysis and quantum mechanics. I was elected to a Fellowship of the Learned Society of Wales in 2010.

Table of Contents

1. Linear operators in Banach spaces2. Entropy numbers, s-numbers, and eigenvalues3. Unbounded linear operators4. Sesqilinear forms in Hilbert spaces5. Sobolve spaces6. Generalized Dirichlet and Neumann boundary-value problems7. Second-order differantial operators on arbitary open sets8. Capacity and compactness criteria9. Essential spectra10. Essential spectra of general second-order differential operators11. Global and asymptotic estimates for the eigenvalues12. Estimates of the singular valuesBibliography

Editorial Reviews

"The abstract notions are beautifully presented... this is a complex, masterfully written research monograph suitable both for students as well as researchers." — John Schmeelk, zbMATH

From the Publisher