Results 111 to 120 of about 193,737 (236)

When is a semigroup a group? [PDF]

, 2015
A well-known necessary and sufficient condition for the operator A to be the infinitesimal generator of a strongly continuous (C0) group is that both A and -A generate a C0-semigroup.
Zwart, Hans, Zwart, Hans; id_orcid
core  

THE POSITIVE FACTOR OF A SUBNORMAL SEMIGROUP

, 2014
. Consider a strongly continuous semigroup (St) of operators on a Hilbert space H and the polar decomposition S t = UtP t of the semigroup. In this paper, a study is initiated of the positive factor (Pt) of (St).
Mary Embry-wardrop
core  

The growth of a semigroup and its Cayley transform [PDF]

, 2011
Let $A$ be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on a Hilbert space. We show that the powers of the Cayley transform of $A$ are bounded by a constant times $\log (n+1)$.
Besseling, N.C., Zwart, Heiko J.; id_orcid, Zwart, Heiko J.   +2 more
core  

Existence and asymptotic stability of periodic solutions for a class of neutral delayed evolution equation

Demonstratio Mathematica
The purpose of this work is to study the existence and asymptotic stability of ω-periodic mild solutions to a class of neutral delayed evolution equation in Banach space X ddt(z(t)−cz(t−δ))+A(z(t)−cz(t−δ))=f(t,z(t),z(t−τ)),t∈R, $$\frac{\text{d}}{\mathrm ...
Yang Shengbin, Li Yongxiang, Wang Dan
doaj   +1 more source

On the construction of the square root for some differential operators

Современная математика: Фундаментальные направления
Using the Balakrishnan-Yosida approach to constructing fractional powers of linear operators in a Banach space by means of strongly continuous semigroups with densely defined generating operators, in this paper, a similar scheme is presented for ...
V. A. Kostin, D. V. Kostin, M. N. Silaeva   +2 more
doaj   +1 more source

On Landau-Kato inequalities via semigroup orbits

, 2023
Let $\omega>0$. Given a strongly continuous semigroup $\{e^{tA}\}$ on a Banach space and an element $f\in\mathbf{D}(A^2)$ satisfying the exponential orbital estimates $$\|e^{tA}f\|\leq e^{-\omega t}\|f\| \quad\text{and}\quad \|e^{tA}A^2f\|\leq e^{-\omega
Lian, Yanlu, Xue, Fei, Huang, Yi C.
core  

A singular perturbation problem in integrodifferential equations

Electronic Journal of Differential Equations, 1993
Consider the singular perturbation problem for $$varepsilon ^2 u'' (t;varepsilon ) + u'(t;varepsilon ) = Au(t;varepsilon )+int_0^t K(t-s)Au(s;varepsilon),ds+ f(t;varepsilon ),,$$ where $tgeq 0$, $u(0;varepsilon ) = u_0 (varepsilon )$, $u'(0;varepsilon ) =
James Liu
doaj  

Well-posedness and stability analysis of hybrid feedback systems using Shkalikov's theory [PDF]

Opuscula Mathematica, 2006
The modern method of analysis of the distributed parameter systems relies on the transformation of the dynamical model to an abstract differential equation on an appropriately chosen Banach or, if possible, Hilbert space.
Piotr Grabowski
doaj  

Unbounded well-bounded operators, strongly continuous semigroups and the Laplace transform

, 1992
Suppose A is a (possibly unbounded) linear operator on a Banach space. We show that the following are equivalent. (1) A is well-bounded on [0,∞). (2) -A generates a strongly continuous semigroup ${e^{-sA}}_{s≤0}$ such that ${(1/s^2)e^{-sA}}_{s>0}$ is ...
deLaubenfels, Ralph
core  

Weighted asymptotic behavior of solutions to semilinear integro-differential equations in Banach spaces

Electronic Journal of Differential Equations, 2014
In this article, we study weighted asymptotic behavior of solutions to the semilinear integro-differential equation $$ u'(t)=Au(t)+\alpha\int_{-\infty}^{t}e^{-\beta(t-s)}Au(s)ds+f(t,u(t)), \quad t\in \mathbb{R}, $$ where $\alpha, \beta \in \mathbb ...
Yan-Tao Bian, Yong-Kui Chang, Juan J. Nieto   +2 more
doaj