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Linear systems can be regarded as a causal shift-invariant operator on a Hilbert space of signals, and by doing so this book presents an introduction to the common ground between operator theory and linear systems theory. The book therefore includes material on pure mathematical topics such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be entirely suitable for a course in functional analysis; at the same time, the book includes applications to partial differential equations, to the stability and stabilization of linear systems, to power signal spaces (including some recent material not previously available in books), and to delay systems, treated from an input/output point of view. Suitable for students of analysis, this book also acts as an introduction to a mathematical approach to systems and control for graduate students in departments of applied mathematics or engineering.

Linear operators. --- Linear systems. --- Systems, Linear --- Differential equations, Linear --- System theory --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory

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This book - an outgrowth of a topical summer school - sets out to introduce non-specialists from physics and engineering to the basic mathematical concepts of approximation and Fourier theory. After a general introduction, Part II of this volume contains basic material on the complex and harmonic analysis underlying the further developments presented. Part III deals with the essentials of approximation theory while Part IV completes the foundations by a tour of probability theory. Part V reviews some major applications in signal and control theory. In Part VI mathematical aspects of dynamical systems theory are discussed. Part VII, finally, is devoted to a modern approach to two physics problems: turbulence and the control and noise analysis in gravitational waves measurements.

Harmonic analysis. --- Approximation theory. --- Analyse harmonique --- Théorie de l'approximation --- Engineering. --- Systems theory. --- Mathematical physics. --- Physics. --- Control Engineering. --- Systems Theory, Control. --- Complexity. --- Mathematical Methods in Physics. --- Harmonic analysis --- Approximation theory --- Theory of approximation --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Natural philosophy --- Philosophy, Natural --- Physical mathematics --- Physics --- Construction --- Mathematics --- System theory. --- Statistical physics. --- Dynamical systems. --- Control engineering. --- Robotics. --- Mechatronics. --- Control, Robotics, Mechatronics. --- Statistical Physics, Dynamical Systems and Complexity. --- Complex Systems. --- Statistical Physics and Dynamical Systems. --- Mathematical statistics --- Systems, Theory of --- Systems science --- Science --- Statistical methods --- Philosophy --- Physical sciences --- Dynamics --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Programmable controllers