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Author:   V.A. Il'in
Publisher:   Springer Science+Business Media
Imprint:   Kluwer Academic/Plenum Publishers
Edition:   1995 ed.
Dimensions:   Width: 17.80cm , Height: 2.40cm , Length: 25.40cm
Weight:   0.960kg
ISBN:  

9780306110375

ISBN 10:   0306110377
Pages:   390
Publication Date:   31 August 1995
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1. Expansion in the Fundamental System of Functions of the Laplace Operator.- 1.1 Fundamental Systems of Functions and Their Properties.- 1.2 Fractional Kernels.- 1.3 Estimate for the Remainder Term of a Spectral Function in the Metric L2 and the Resulting Corollaries.- 1.4 Exact Conditions for the Localization and Uniform Convergence of Expansions with Respect to an Arbitrary FSF in the Sobolev-Liouville Classes.- 1.5 On the Potential Generalization of the Theory.- Comments on Chapter 1.- 2. Spectral Decompositions Corresponding to an Arbitrary Self-Adjoint Nonnegative Extension of the Laplace Operator.- 2.1 Self-Adjoint Nonnegative Extensions of Elliptic Operators. Ordered Spectral Representations of the Space L2. Classes of Differentiate Functions of N Variables.- 2.2 Formulation and Analysis of Main Results.- 2.3 Certain Properties of the Fundamental Functions of an Arbitrary Ordered Spectral Representation in the Space L2.- 2.4 Proof of Negative Theorem 2.1.- 2.5 Proof of Positive Theorem 2.3.- 2.6 Estimate for the Remainder Term of the Riesz Means of a Spectral Function in the Metric L2.- 2.7 Estimate for the Remainder Term of the Riesz Means of a Spectral Function in the Metric L2.- Comments on Chapter 2.- 3. On the Riesz Equisummability of Spectral Decompositions in the Classical and the Generalized Sense.- 3.1 On the Riesz Equisummability of Spectral Decompositions in the Classical Sense.- 3.2 On the Riesz Equisummability of Spectral Decompositions in the Generalized Sense.- Comments on Chapter 3.- 4. Self-Adjoint Nonnegative Extensions of an Elliptic Operator of Second Order.- 4.1 Ancillary Propositions about Fundamental Functions.- 4.2 Theorems of Negative Type.- 4.3 Theorems of Positive Type.- Comments on Chapter 4.- Appendix 1. Conditions for the Uniform Convergence of Multiple Trigonometric Fourier Series with Spherical Partial Sums.- 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.- Epilogue.- References.

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