Written in English
Thesis (M. Sc.)--The Queen"s University of Belfast, 1967.
|The Physical Object|
Get this from a library! Stability of operators and operator semigroups. [Tanja Eisner] -- This book systematically studies the asymptotic behavior, in particular ""stability"" in some sense, for discrete and continuous linear dynamical systems on Banach spaces. Of special concern is. PDF | On Jan 1, , Ralph Chill and others published Stability of Operator Semigroups: Ideas and Results | Find, read and cite all the research you need on ResearchGate In book. Stability Conditions for Perturbed Semigroups on a Hilbert Space via Commutators — / References  R. Curtain, H. Zwart, Introduction to Inﬁnite-Dimensional Systems Theory, . Thus the book is much broader in scope than existing books on asymptotic behavior of semigroups. Included is a solid collection of examples from different areas of analysis, PDEs, and dynamical systems. This is the first monograph where the spectral theory of infinite dimensional linear skew-product flows is described together with its.
Desch W., Schappacher W. () Linearized stability for nonlinear semigroups. In: Favini A., Obrecht E. (eds) Differential Equations in Banach Spaces. Lecture . Ulam Stability of Operators presents a modern, unified, and systematic approach to the field. Focusing on the stability of functional equations across single variable, difference equations, differential equations, and integral equations, the book collects, compares, unifies, complements, generalizes, and updates key results. The main theme of the book is the spectral theory for evolution operators and evolution semigroups, a subject tracing its origins to the classical results of J. Mather on hyperbolic dynamical systems and J. Howland on nonautonomous Cauchy problems. This unifying idea connects various questions in stability of semigroups, infinite-dimensional hyperbolic linear skew-product flows, translation Banach algebras, transfer operators, stability radii in control theory, Lyapunov exponents, magneto-dynamics and the book is much broader in scope than existing books on asymptotic.
Book Description. Motivated by applications to control theory and to the theory of partial differential equations (PDE's), the authors examine the exponential stability and analyticity of C0-semigroups associated with various dissipative systems. They present a unique, systematic approach in which they prove exponential stability by combining a. In this paper the theory of evolution semigroups is developed and used to provide a framework to study the stability of general linear control systems. These include autonomous and nonautonomous sy. Book Description. In this masterful study, the author sets forth a unique treatment of the stability and instability of the periodic equilibria of partial differential equations as they relate to the notion of direct integrals. Readers with some basis in functional analysis-notably semigroups-and measure theory can strengthen their. Lyapunov functions are common in proving stability of nonlinear differential equations, but they can also be used to characterize stability properties of semigroups, see [5, Theorem ] for exponential stability. In the following necessary and sufficient condition for strong stability is given. Theorem 2.