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ISBN: 0521825849 9780521825849 9780511543197 0511082088 9780511082085 0511081634 9780511081637 0511543190 0511298404 9780511298400 1107137802 128043113X 9786610431137 0511171315 0511197012 Year: 2005 Volume: 103 Publisher: Cambridge, UK New York Cambridge University Press
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Many infinite-dimensional linear systems can be modelled in a Hilbert space setting. Others, such as those dealing with heat transfer or population dynamics, need to be set more generally in Banach spaces. This is the first book dealing with well-posed infinite-dimensional linear systems with an input, a state, and an output in a Hilbert or Banach space setting. It is also the first to describe the class of non-well-posed systems induced by system nodes. The author shows how standard finite-dimensional results from systems theory can be extended to these more general classes of systems, and complements them with new results which have no finite-dimensional counterpart. Much of the material presented is original, and many results have never appeared in book form before. A comprehensive bibliography rounds off this work which will be indispensable to all working in systems theory, operator theory, delay equations and partial differential equations.
System theory --- Linear systems --- Linear systems. --- System theory. --- Systems, Theory of --- Systems science --- Science --- Systems, Linear --- Differential equations, Linear --- Philosophy
ISBN: 0521372895 9780511662805 0511662807 9781107088054 1107088054 9780521372893 9780521103060 1139884484 0511948557 1107102715 0521103061 1107094232 1107091128 Year: 1990 Volume: 34 Publisher: Cambridge [England] New York Cambridge University Press
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The rapid development of the theories of Volterra integral and functional equations has been strongly promoted by their applications in physics, engineering and biology. This text shows that the theory of Volterra equations exhibits a rich variety of features not present in the theory of ordinary differential equations. The book is divided into three parts. The first considers linear theory and the second deals with quasilinear equations and existence problems for nonlinear equations, giving some general asymptotic results. Part III is devoted to frequency domain methods in the study of nonlinear equations. The entire text analyses n-dimensional rather than scalar equations, giving greater generality and wider applicability and facilitating generalizations to infinite-dimensional spaces. The book is generally self-contained and assumes only a basic knowledge of analysis. The many exercises illustrate the development of the theory and its applications, making this book accessible to researchers in all areas of integral and differential equations.
Integral equations --- Volterra equations --- Functional equations --- Functional equations. --- Integral equations. --- Volterra equations. --- 517.9 --- 519.6 --- 681.3*G19 --- 681.3*G19 Integral equations: Fredholm equations; integro-differential equations; Volterra equations (Numerical analysis) --- Integral equations: Fredholm equations; integro-differential equations; Volterra equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Equations, Functional --- Functional analysis --- Equations, Integral --- Equations, Volterra --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis
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