Spectral theory and differential operators

By:

Davies, Edward Brian

Material type: Book

BookSeries: CPublication details: Cambridge: Cambridge University Press, 1996.Description: ix, 182 p. : ill. ; pb, 24 cmISBN:

9780521587105

Subject(s):

DDC classification:

515.7222 DAV

Summary: 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.

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Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar General Stacks	General	515.7222 DAV (Browse shelf(Opens below))	1	Available		030167

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Previous	515.7 RAY Elementary introduction to the theory of pseudodifferential operators	515.72 PAL Reconstructive integral geometry	515.72 TRE Introduction to pseudodifferential and fourier integral operators ,Vol. 2 :	515.7222 DAV Spectral theory and differential operators	515.723 MIL Integral transforms in applied mathematics	515.723 WID Laplace transform	515.724 TRE Introduction to pseudodifferential and fourier integral operators, Vol.1 :	Next

Includes bibliographical references (p. 178) and 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.

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