An Introduction to Identification Problems via Functional Analysis

Parameter identification in linear ordinary differential equations; examples of inverse problems; 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 to problem; 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; 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; 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; 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; 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. (Part contents)