C₀-semigroups and applications /

The book contains a unitary and systematic presentation of both classical and very recent parts of a fundamental branch of functional analysis: linear semigroup theory with main emphasis on examples and applications. There are several specialized, but quite interesting, topics which didn't find...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Vrabie, I. I. (Ioan I.), 1951-
Formato: Electrónico eBook
Idioma:Inglés
Romanian
Publicado: Amsterdam ; Boston : Elsevier Science, 2003.
Edición:1st edition
Colección:North-Holland mathematics studies ; 191.
Temas:
Semigroups of operators.
Semi-groupes d'op�erateurs.
MATHEMATICS > Functional Analysis.
Acceso en línea:Texto completo
Texto completo
Texto completo
Tabla de Contenidos:
  • Cover
  • Contents
  • Preface
  • Chapter 1. Preliminaries
  • 1.1. Vector-Valued Measurable Functions
  • 1.2. The Bochner Integral
  • 1.3. Basic Function Spaces
  • 1.4. Functions of Bounded Variation
  • 1.5. Sobolev Spaces
  • 1.6. Unbounded Linear Operators
  • 1.7. Elements of Spectral Analysis
  • 1.8. Functional Calculus for Bounded Operators
  • 1.9. Functional Calculus for Unbounded Operators
  • Problems
  • Notes
  • Chapter 2. Semigroups of Linear Operators
  • 2.1. Uniformly Continuous Semigroups
  • 2.2. Generators of Uniformly Continuous Semigroups
  • 2.3. C0-Semigroups. General Properties
  • 2.4. The Infinitesimal Generator
  • Problems
  • Notes
  • Chapter 3. Generation Theorems
  • 3.1. The Hille-Yosida Theorem. Necessity
  • 3.2. The Hille-Yosida Theorem. Sufficiency
  • 3.3. The Feller-Miyadera-Phillips Theorem
  • 3.4. The Lumer-Phillips Theorem
  • 3.5. Some Consequences
  • 3.6. Examples
  • 3.7. The Dual of a C0-Semigroup
  • 3.8. The Sun Dual of a C0-Semigroup
  • 3.9. Stone Theorem
  • Problems
  • Notes
  • Chapter 4. Differential Operators Generating C0- Semigroups
  • 4.1. The Laplace Operator with Dirichlet Boundary Condition
  • 4.2. The Laplace Operator with Neumann Boundary Condition
  • 4.3. The Maxwell Operator
  • 4.4. The Directional Derivative
  • 4.5. The Schr�odinger Operator
  • 4.6. The Wave Operator
  • 4.7. The Airy Operator
  • 4.8. The Equations of Linear Thermoelasticity
  • 4.9. The Equations of Linear Viscoelasticity
  • Problems
  • Notes
  • Chapter 5. Approximation Problems and Applications
  • 5.1. The Continuity of A?etA
  • 5.2. The Chernoff and Lie-Trotter Formulae
  • 5.3. A Perturbation Result
  • 5.4. The Central Limit Theorem
  • 5.5. Feynman Formula
  • 5.6. The Mean Ergodic Theorem
  • Problems
  • Notes
  • Chapter 6. Some Special Classes of C0-Semigroups
  • 6.1. Equicontinuous Semigroups
  • 6.2. Compact Semigroups
  • 6.3. Differentiable Semigroups
  • 6.4. Semigroups with Symmetric Generators
  • 6.5. The Linear Delay Equation
  • Problems
  • Notes
  • Chapter 7. Analytic Semigroups
  • 7.1. Definition and Characterizations
  • 7.2. The Heat Equation
  • 7.3. The Stokes Equation
  • 7.4. A Parabolic Problem with Dynamic Boundary Conditions
  • 7.5. An Elliptic Problem with Dynamic Boundary Conditions
  • 7.6. Fractional Powers of Closed Operators
  • 7.7. Further Investigations in the Analytic Case
  • Problems
  • Notes
  • Chapter 8. The Nonhomogeneous Cauchy Problem
  • 8.1. The Cauchy Problem u' = Au + f, u(a) =?
  • 8.2. Smoothing Effect. The Hilbert Space Case
  • 8.3. An Approximation Result
  • 8.4. Compactness of the Solution Operator from LP(a, b ; X
  • 8.5. The Case when (?I
  • A) -1 is Compact
  • 8.6. Compactness of the Sol.

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