Spectral Analysis Of Differential Operators : Interplay Between Spectral And Oscillatory Properties.

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This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigat...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Rofe-Beketov, Fedor S.
Otros Autores: Kholkin, Aleksandr M.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore : World Scientific, 2005.
Colección:World Scientific monograph series in mathematics ; v. 7.
Temas:
Differential operators.
Hilbert space.
Operator theory.
Selfadjoint operators.
Spectral theory (Mathematics)
Opérateurs différentiels.
Espace de Hilbert.
Théorie des opérateurs.
Opérateurs auto-adjoints.
Spectre (Mathématiques)
Differential operators
Hilbert space
Operator theory
Selfadjoint operators
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Contents
  • Foreword
  • Preface
  • Acknowledgments
  • Introduction
  • 1. Relation Between Spectral and Oscillatory Properties for the Matrix Sturm-Liouville Problem
  • 1.1 Problem on a Finite Interval
  • 1.2 Problem on the Half-Line
  • 1.3 Bibliographical Comments
  • 1.3.1 An Example of the Operator of (1.1)(1.3) Type with the Purely Absolutely Continuous Spectrum
  • 1.3.2 Oscillatory Theory of Partial Differential Equations
  • 1.3.3 Bochner Integral
  • 2. Fundamental System of Solutions for an Operator Differential Equation with a Singular Boundary Condition
  • 2.1 Separated Self-Adjoint Boundary Conditions
  • 2.2 A Construction for the Fundamental Solution of the Boundary-Value Problem
  • 2.3 Self-consistency of the Fundamental Solution of the Self- Adjoint Problem and the Evolution of the Corresponding Hermitian Relation (or Lagrangian Plane in H @ H)
  • 2.4 A Different Construction for the Fundamental Solution of the Boundary-Value Problem
  • 2.5 Bibliographical Comments
  • 3. Dependence of the Spectrum of Operator Boundary Problems on Variations of a Finite or Semi-Infinite Interval
  • 3.1 Dependence of Eigenvalues and the Greatest Lower Bound of the Spectrum for a Semi-Bounded Below Differential Operator on Variations of the Interval
  • 3.2 Continuity and Monotonicity of the Greatest Lower Bound of the Essential Spectrum for Semi-Bounded Below Differential Operators
  • 3.3 Bibliographical Comments
  • 4. Relation Between Spectral and Oscillatory Properties for Operator Differential Equations of Arbitrary Order
  • 4.1 Oscillatory Theorem for Operator Differential Equations of Even Order
  • 4.2 Comparison and Alternation Theorems
  • 4.3 Multiplicative Representation of Positive Differential Operators and Its Applications
  • 4.4 Discrete Levels in the Gaps of the Essential Spectrum
  • 4.5 Bibliographical Comments
  • 4.5.1 Symplectic Interpretation of Sturm-Type Theorems and Their Operator-Theoretical Proofs
  • 5. Self-Adjoint Extensions of Systems of Differential Equations of Arbitrary Order on an Infinite Interval in the Absolutely Indefinite Case
  • 5.1 A Description of Self-Adjoint Extensions of Differential Operators of Arbitrary Order with Operator-Valued Coefficients on an Infinite Interval
  • 5.2 Parametrization of the Characteristic Operator Function
  • 5.3 Bibliographical Comments
  • 5.3.1 Everitt-Zettl Problem, Brusentsevs Example and Two Open Questions
  • 5.3.2 On the Deficiency Indices of Scalar Symmetric Dif- ferential Operators of General Kind on the Half-Axis (Solved and Unsolved Questions)
  • 5.3.3 Kogan-Rofe-Beketovs Asymptotic Theorems and Deficiency Indices of Symmetric Differential Operator
  • 5.3.4 R.C. Gilberts Class of Formally Self-Adjoint Ordi- nary Differential Operators Whose Deficiency Numbers Differ by an Arbitrary Pre-Assigned Positive Integer
  • 5.3.5 Deficiency Indices of Symmetric Differential Systems of the First and Arbitrary Orders and Some Open Questions
  • 5.3.6 Some Comments on Hilberts 21-st Problem and Bolibrukh Counterexample
  • 5.3.7 Some Comments on Section 5.2
  • 5.3.8 Characteristic Properties of Weyl Solutions for the Sturm-Liouville and Dirac Equations. V.A. Marchenkos Theorems
  • 6. Discrete Levels in Spectral Gaps of Perturbed Schrodinger and Hill Operators
  • 6.1 Factorized Phase Matrix of the Perturbed System and the Discrete Spectrum in Gaps of the Continuous Spectrum
  • 6.2 Generalization of D Alembert-Liouville-Ostrogradsky For- mula and Its Application to Growth Estimates for Solutions of Canonical Almost Periodic Systems
  • T$19058.

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