2 edition of **Stability in semigroups.** found in the catalog.

Stability in semigroups.

Liam O"Carroll

- 135 Want to read
- 13 Currently reading

Published
**1967**
.

Written in English

**Edition Notes**

Thesis (M. Sc.)--The Queen"s University of Belfast, 1967.

The Physical Object | |
---|---|

Pagination | 1 v |

ID Numbers | |

Open Library | OL19420942M |

a family of strongly continuous semigroups on a Hilbert space depending on a complex parameter 2 ˆC, that is, fT(t;)g t>0, 2, let us assume that -dependent constants L() and N() in (), () are bounded from above uni-formly for 2. We then conclude that the constants M() in () are bounded from above uniformly for 2. Cambridge Core academic books, journals and resources for Probability theory and stochastic processes. Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites.

of semigroups (and also Volterra equations) and to more "qualitative" forms (in dividual stability, estimates etc.). For an account of these developments see the book [34] and the surveys [4], [46]. But most of extensions follow the principle "the smaller the set о (А) П iE, the better the asymptotic properties of the orbits of (T(i))tj>0". Differentiable semigroups. A strongly continuous semigroup T is called eventually differentiable if there exists a t 0 > 0 such that T(t 0)X⊂D(A) (equivalently: T(t)X ⊂ D(A) for all t ≥ t 0) and T is immediately differentiable if T(t)X ⊂ D(A) for all t > Every analytic semigroup is immediately differentiable. An equivalent characterization in terms of Cauchy problems is the.

The book of Lasota and Mackey [27] is an excellent survey of many results on this subject. Semigroups of Markov operators and semigroups: asymptotic stability and sweeping. Theorems concerning asymptotic stability and sweeping allow us to formulate the Foguel alternative. This alternative says that under suitable conditions a Markov operator. the theory of stability of ordinary differential equations contains the germs for a theory of stability of nonlinear evolution semigroups This book is devoted to a self-contained systematic exposition of these matters and incorporates many of the author's own substantial results in .

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This book is about stability of linear dynamical systems, discrete and continuous. More precisely, we discuss convergence to zero of strongly continuous semigroups of operators and of powers of a bounded linear operator, both with respect to different topologies.

The discrete and the continuous cases are treated in parallel, and we Cited by: This book is about stability of linear dynamical systems, discrete and continuous.

More precisely, we discuss convergence to zero of strongly continuous semigroups of operators and of powers of a bounded linear operator, both with respect to different topologies. 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 [1] 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. 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. The authors use a wide range of methods and offer a unique : $ We study polynomial and exponential stability for C 0-semigroups using the recently developed theory of operator-valued (L p, L q) Fourier multipliers.

We characterize polynomial decay of orbits of a C 0-semigroup in terms of the (L p, L q) Fourier multiplier properties of its resolvent. Using this characterization we derive new polynomial decay rates. Linear stability in an ideal incompressible fluid.

Comm. Math. Phys. () (with M. Vishik) Operator valued Fourier multipliers and stability of strongly continuous semigroups, Integral Equations Operator Theory 51 () (with F. Raebiger). Books, survey and expository papers (peer reviewed) Schnaubelt, Semigroups for nonautonomous Cauchy problems.

In: K. Engel and R. Nagel, \One{Parameter Semigroups for Linear Evolution Equations," Springer-Verlag, Polynomial asymptotic stability of operator semigroups.

Math. Nachr. (), { Y. Latushkin, J. Pruss and R. compact semigroups, we recall the powerful notion of the cogenerator of a C 0-semigroup. Finally, we present one of our main concepts for the investigation of stability of C 0-semigroups, the Laplace inversion formula, which can also be seen as an extension of the Dunford functional calculus for exponential functions.

“This book is based on the author’s lecture notes in which the more advanced parts concentrated on spectral representations. There is also a presentation of a well-known stability theorem for semigroups under countable spectral conditions. The increased variety of topics covered will make the book more useful.

This book presents a systematic account of the theory of asymptotic behaviour of semigroups of linear operators acting in a Banach space. The focus is on the relationship between asymptotic behaviour of the semigroup and spectral properties of Price: $Ulam stability theory is multifaceted.

The above definitions and results will be used in the next sections, but much more information concerning the state-of-the-art can be found in [1,4,5] and the references nt publications concerning the Ulam stability for the composition of operators are [] ([Chapter 2]), [4,6,7]; our paper is motivated by these existing results and, to a.

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 hydro-dynamics.

Thus the book is much broader in scope than existing books on asymptotic Reviews: 1.