Spectral Theory of Differential Operators : Self-Adjoint Differential Operators

By: V.A. Il'in

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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.

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Expansion in the Fundamental System of Functions of the Laplace Operator	p. 1
Spectral Decompositions Corresponding to an Arbitrary Self-Adjoint Nonnegative Extension of the Laplace Operator	p. 83
On the Riesz Eguisummability of Spectral Decompositions in the Classical and the Generalized Sense	p. 197
Self-Adjoint Nonnegative Extensions of an Elliptic Operator of Second Order	p. 253
Appendix 1. Conditions for the Uniform Convergence of Multiple Trigonometric Fourier Series with Spherical Partial Sums	p. 351
Appendix 2. Conditions for the Uniform Convergence of Decompositions in Eigenfunctions of the First, Second, and Third Boundary-Value Problems for an Elliptic Operator of Second Order	p. 355
Epilogue	p. 367
References	p. 379
Index	p. 387
Table of Contents provided by Blackwell. All Rights Reserved.

Spectral Theory of Differential Operators : Self-Adjoint Differential Operators

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Hardcover

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