Spectral Theory of Differential Operators: Self-Adjoint Differential Operators / Edition 1

by V.A. Il'in

Overview

In this fully-illustrated textbook, the author examines the spectral theory of self-adjoint elliptic operators. Chapters focus on the problems of convergence and summability of spectral decompositions about the fundamental functions of elliptic operators of the second order. The author's work offers a novel method for estimation of the remainder term of a spectral function and its Riesz means without recourse to the traditional Carleman technique and Tauberian theorem apparatus.

Product Details

ISBN-13:	9780306110375
Publisher:	Springer US
Publication date:	08/31/1995
Edition description:	1995
Pages:	390
Product dimensions:	7.01(w) x 10.00(h) x (d)

Table of Contents

Introduction. Nomenclature. The Expansion in Fundamental System of Functions of the Laplace Operator. The Spectral Expansions Related to an Arbitrary Selfadjoint Nonnegative Extension of the Laplace Operator. On the Riesz Equisummability of Spectral Decompositions in the Classical Sense and Generalized Sense. Selfadjoint Nonnegative Extensions of the Elliptic Operator of the Second Order. Appendix 1: Conditions for Uniform Convergence of Multiple Trigonometric Fourier Series with Spheric Partial Sums. Appendix 2: Conditions for Uniform Convergence of Eigenfunction Expansions of the First, Second, and Third Boundary Problems for the Elliptic Operator of Second Order. Epilogue. Index.

Editorial Reviews

Demonstrates the efficiency of the author's novel techniques based on the mean-value theorems for regular solutions of elliptic equations with a spectral parameter. Four chapters discuss functions of the Laplace operator and its arbitrary self-adjoint nonnegative extensions, the Reisz equisummability of spectral decompositions, and the technique's application to a general self-adjoint elliptic operator L of second order with smooth coefficients. Appendices deal with situations in which the function to be expanded is not compactly supported. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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