Introduction to Identification
Problems via Functional Analysis
By A. Lorenzi
December 2001
VSP
ISBN: 90-6764-349-1
254 pages
$255.00 hardcover
Contents:
-
- 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 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
Inverse & Ill-Posed Problems Series
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