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Spectral Theory and Differential Operators : Cambridge Studies in Advanced Mathematics (Paperback) - E. Brian Davies

Spectral Theory and Differential Operators

Cambridge Studies in Advanced Mathematics (Paperback)

Paperback Published: 23rd December 1996
ISBN: 9780521587105
Number Of Pages: 196

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This book is an introduction to the theory of partial differential operators. It assumes that the reader has a knowledge of introductory functional analysis, up to the spectral theorem for bounded linear operators on Banach spaces. However it describes the theory of Fourier transforms and distributions as far as is needed to analyse the spectrum of any constant coefficient partial differential operator. A completely new proof of the spectral theorem for unbounded self-adjoint operators is followed by its application to a variety of second order elliptic differential operators, from those with discrete spectrum to Schrodinger operators acting on L2(RN), The book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques.This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on the subject.

' ... a new approach to the spectral theorem for self-adjoint unbounded operators ... For readers with standard background in functional analysis and bounded operator theory the book can serve as a missing link to the more advanced literature.' Monatshefte fur Mathematik ' ... a concise and nicely written introduction to many important areas of this vast mathematical discipline ... This short book (180 pages) will be very useful both to students and researchers working in related areas of mathematics and physics.' European Mathematical Society

The fundamental ideas
The spectral theorem
Translation invariant operators
The variation methods
Further spectral results
Dirichlet boundary conditions
Neumann boundary conditions
Schrdinger operators
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521587105
ISBN-10: 0521587107
Series: Cambridge Studies in Advanced Mathematics (Paperback)
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 196
Published: 23rd December 1996
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.84 x 15.14  x 1.09
Weight (kg): 0.27