Spectral Theory of Differential Operators

Name: Spectral Theory of Differential Operators
SKU: 9780306110375
Price: 719 SEK
Availability: InStock
Author: V.A. Il'in
ISBN: 9780306110375

Self-Adjoint Differential Operators

Inbunden, Engelska, 1995

AvV.A. Il'in

719 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

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.

Produktinformation

Utgivningsdatum1995-08-31
Mått178 x 254 x 24 mm
Vikt930 g
FormatInbunden
SpråkEngelska
Antal sidor390
Upplaga1995
FörlagKluwer Academic Publishers Group
ISBN9780306110375

Tillhör följande kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

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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Spectral Theory of Differential Operators

Self-Adjoint Differential Operators

Inbunden, Engelska, 1995

AvV.A. Il'in

719 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

Produktinformation

Utgivningsdatum1995-08-31
Mått178 x 254 x 24 mm
Vikt930 g
FormatInbunden
SpråkEngelska
Antal sidor390
Upplaga1995
FörlagKluwer Academic Publishers Group
ISBN9780306110375

Tillhör följande kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

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.