Includes bibliographical references and index.

Cover13; -- Functional Analysis in Modern Applied Mathematics -- Copyright Page -- Contents -- Introduction -- PART I: Basic Functional Analysis -- Chapter 1. NORMED LINEAR SPACES -- Chapter 2. INTEGRATION THEORY FOR REAL-VALUED FUNCTIONS -- Chapter 3. LINEAR TRANSFORMATIONS -- Chapter 4. HILBERT SPACES -- Chapter 5. PROBABILITY THEORY -- Chapter 6. CALCULUS IN BANACH SPACES -- Chapter 7. TOPOLOGICAL SPACES -- Part II: Analysis of Abstract Equations -- Chapter 8. DIFFERENTIAL EQUATIONS -- 8.1 Ordinary differential equations -- 8.2 Stochastic differential equations -- 8.3 Differential delay equations -- 8.4 Partial differential equations -- 8.5 Abstract equations -- 8.6 Semigroup theory -- 8.7 Solution of inhomogeneous abstract evolution equations -- Chapter 9. SPECTRAL THEORY AND APPLICATIONS -- 9.1 Spectral theory in finite dimensions -- 9.2 Spectrum of closed linear operators on a normed linear space -- 9.3 Spectral theory for compact normal operators -- 9.4 Spectral decomposition for unbounded linear operators -- Part III: Applications -- Chapter 10. STABILITY THEORY -- 10.1 Liapunov stability for ordinary differential equations -- 10.2 Stability properties of operators : perturbation theory -- Chapter 11. LINEAR SYSTEMS THEORY -- 11.1 Controllability -- 11.2 Stability -- 11.3 Observability -- 11.4 Linear quadratic control problems -- 11.5 Filtering -- 11.6 Time optimal control -- Chapter 12. OPTIMIZATION PROBLEMS -- 12.1 Minimization of coercive bilinear forms -- 12.2 Least squares minimization in a Hilbert space -- 12.3 Unconstrained Calculus of Variations problems -- 12.4 Minimization under equality constraints -- 12.5 Minimization with inequality constraints -- 12.6 Optimal control theory -- Chapter 13. NUMERICAL METHODS -- 13.1 General principles and introduction -- 13.2 Linear equations -- 13.3 Nonlinear equations -- 13.4 Approximation theory -- 13.5 Numerical solution of optimization problems -- Chapter 14. INFINITE DIMENSIONAL LINEAR SYSTEMS THEORY -- 14.1 Controllability -- 14.2 Observability -- 14.3 The quadratic cost control problem for evolution equations -- 14.4 A direct approach to the quadratic cost control problem -- INDEX.

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;<BR id="CRLF">methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and<BR id="CRLF">methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.<BR id="CRLF"><BR id="CRLF">As a result, the book represents a blend of new methods in general computational analysis, <BR id="CRLF">and specific, but also generic, techniques for study of systems theory ant its particular<BR id="CRLF">branches, such as optimal filtering and information compression.

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