Spectral theory and differential operators / E. B. Davies

Auteur: Davies, Edward Brian (1944-) - AuteurType de document: MonographieCollection: Cambridge studies in advanced mathematics ; 42Langue: anglaisPays: Grande BretagneÉditeur: Cambridge : Cambridge university press, cop. 1995Description: 1 vol. (IX-182 p.) : fig. ; 23 cm ISBN: 0521472504 ; rel. Résumé: 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 Schrödinger 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. (Source : CUP).Bibliographie: Bibliogr. p. 178. Index. Sujets MSC: 47-02 Operator theory -- Research exposition (monographs, survey articles)
47A10 Operator theory -- General theory of linear operators -- Spectrum, resolvent
47E05 Operator theory -- Ordinary differential operators -- Ordinary differential operators
47F05 Operator theory -- Partial differential operators -- Partial differential operators
34L05 Ordinary differential equations -- Ordinary differential operators -- General spectral theory
35P05 Partial differential equations -- Spectral theory and eigenvalue problems -- General topics in linear spectral theory
35J10 Partial differential equations -- Elliptic equations and systems -- Schrödinger operator
En-ligne: sommaire
Location Call Number Status Date Due
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Bibliogr. p. 178. Index

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 Schrödinger 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. (Source : CUP)

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