An introduction to identification problems via functional analysis /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Lorenzi, A. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Utrecht ; Boston : VSP, 2001.
Colección:Inverse and ill-posed problems series.
Temas:
Inverse problems (Differential equations)
Functional analysis.
Problèmes inverses (Équations différentielles)
Analyse fonctionnelle.
Functional analysis
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Introduction
  • Chapter 1. Parameter Identification in Linear Ordinary Differential Equations
  • 1.1. Introduction
  • 1.2. Examples of inverse problems
  • 1.3. Appendix. Exponential of a square matrix
  • Chapter 2. Identification Problems in Hilbert Spaces
  • 2.1. An identification problem related to a first-order differential equation
  • 2.2. Analysis of the dependence on the data of the solution ({yn}, λ) to problem (2.1.5), (2.1.6)
  • 2.3. The minimization method
  • 2.4. A further identification problem
  • 2.5. A generalization to the vector case
  • 2.6. An identification problem for a second-order differential equationChapter 3. Proper Riemann Integrals for Banach-valued Functions. Curvilinear Integrals and Banach-valued Holomorphic Functions
  • 3.1. Proper Riemann Integrals: basic properties
  • 3.2. Curvilinear Integrals and Banach-valued Holomorphic Functions
  • Chapter 4. Riemann-Stieltjes Integrals of Banach-valued Functions
  • 4.1. Riemann-Stieltjes integrals over compact intervals
  • Chapter 5. Improper Riemann Integrals for Banach Space-valued functions
  • 5.1. Improper integrals
  • Chapter 6. Banach Algebras and Spectral Analysis for Linear Bounded Operators6.1. Introduction
  • 6.2. Basic properties of the spectrum of an element
  • 6.3. Integration of Banach algebra-valued functions
  • 6.4. Banach algebra-valued holomorphic functions and the spectral theorem
  • Chapter 7. Identifying Parameters in First-Order Partial Differential Equations
  • 7.1. An identification problem relative to a first-order linear partial differential equation
  • 7.2. An identification problem relative to a non-linear first-order partial differential equation
  • Chapter 8. Identification Problems relative to Linear Bounded Operators I8.1. An identification problem relative to a first-order differential equation
  • 8.1.1. The singular case
  • 8.1.2. The supersingular case
  • 8.1.3. Continuous dependence on the data
  • 8.2. An identification problem relative to a second-order differential equation
  • 8.3. A particular case
  • 8.4. An integro-differential identification problem
  • 8.5. A onedimensional integro-differential identification problem
  • Chapter 9. Identification Problems Relative to Linear Bounded Operators II
  • 9.1. An abstract control problem9.2. A concrete example
  • Chapter 10. Analysis of the Continuous Dependence on the Data
  • 10.1. Construction of an abstract model for the analysis of the continuous dependence on the data
  • 10.2. Continuous dependence on the data of the solution to the identification problem (8.4.1)
  • 10.3. Appendix. Gronwallâ€?s generalized inequality
  • Chapter 11. Linear Closed operators and Analytic Semigroups of Linear Bounded Operators
  • 11.1. Linear closed operators
  • 11.2. Resolvent set and spectrum of a linear operator

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