An Introduction to Identification Problems via Functional Analysis

Introduction
Parameter identification in linear ordinary differential equations
Introduction
Examples of inverse problems
Appendix. Exponential of a square matrix
Identification problems in Hilbert spaces
An identification problem related to a first-order differential equation
Analysis of the dependence on the data of the solution (Yn, ?) to problem (2.1.5), (2.1.6)
The minimization method
A further identification problem
A generalization to the vector case
An identification problem for a second-order differential equation
Proper Riemann integrals for Banach-valued functions. Curvilinear integrals and Banach-valued holomorphic functions
Proper Riemann integrals: basic properties
Curvilinear integrals and Banach-valued holomorphic functions
Riemann-Stieltjes integrals for Banach space-valued functions
Rieman-Stieltjes integrals over compact intervals
Improper Riemann integrals for Banach space-valued functions
Improper integrals
Banach algebras and spectral analysis for linear bounded operators
Introduction
Basic properties of the spectrum of an element
Integration of Banach algebra-valued functions
Banach algebra-valued holomorphic functions and the spectral theorem
Identifying parameters in first-order partial differential equations
An identification problem relative to a first-order linear partial differential equation
An identification problem relative to a non-linear first-order partial differential equation
Identification problems relative to linear bounded operators. I
An identification problem relative to a first-order differential equation
The singular case; The supersingular case; Continuous dependence on the data
An identification problem relative to a second-order differential equation
A particular case
An integro-differential identification problem
A one-dimensional integro-differential problem
Identification problems relative to linear bounded operators. II
An abstract control problem
A concrete example
Analysis of the continuous dependence on the data
Construction of an abstract model for the analysis of the continuous dependence on the data
Continuous dependence on the data of the solution to the identification problem (8.4.1)
Appendix. Gronwall's generalized inequality
Linear closed operators and analytic semigroups of linear bounded operators
Linear closed operators
Resolvent set and spectrum of a linear operator
Sectorial operators
Cauchy problems for linear abstract differential equations relative to sectorial operators and applications
Abstract differential equations and analytic semigroups. Application to Cauchy problems
Applications
Identification problems for linear abstract differential equations relative to sectorial operators and applications
An abstract identification problem
An application to a concrete case
An identification problem relative to an abstract non-autonomous first-order differential equation
Analysis of a Cauchy problem with coefficients depending on time only
Analysis of a Cauchy problem with non-homogeneous boundary value conditions on a bounded interval
Solving the identification problem (13.3.1)-(13.3.4)
Bibliography
List of symbols