Results 151 to 160 of about 3,180,909 (182)

Polynomially Compact-Like Strongly Continuous Semigroups

Acta Applicandae Mathematica, 2004
Several results concerning the class of semigroups of operators \((T(t))_{t\geq 0}\) on a Banach space \(X\) such that \(T(s) - I\) is compact for some \(s>0\) are known. The authors study semigroups for which there exists a (nontrivial) polynomial \(p\) such that, for some \(s>0\), \(p(T(s))\) belongs to a two-sided ideal of the algebra \(B(X ...
Latrach, Khalid, Paoli, J. Martin
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$$\Gamma $$-Supercyclicity for Strongly Continuous Semigroups

Complex Analysis and Operator Theory, 2019
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Strongly Continuous Semigroups and Stochastic Representation

Journal of the London Mathematical Society, 2002
Second‐order elliptic operators realized under Dirichlet boundary conditions in bounded domains are shown to generate strongly continuous semigroups in the topology of uniform convergence. The stochastic representation and integral representation with kernel for the strongly continuous semigroups are given.
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Strongly Continuous Semigroups

1998
This chapter is devoted to strongly continuous semigroups of operators. It is well-known that the mentioned semigroups are the basic instrument for investigation of differential equations with constant operators in Banach and Hilbert spaces. Wide classes of autonomous distributed parameter systems are governed by such equations.
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Periodic strongly continuous semigroups

Annali di Matematica Pura ed Applicata, 1977
It is shown that three possible definitions of periodicity of a strongly continuous semigroup are equivalent. A complete characterization of periodicity is obtained in terms of the infinitesimal generator. An example is given to illustrate how the results tie in with the classical theory of periodic continuous functions.
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Maximal asymptotics of certain class of strongly continuous semigroups

2017 25th Mediterranean Conference on Control and Automation (MED), 2017
We consider a class of first order linear differential equations given in infinite-dimensional space. We study asymptotic behavior of individual solutions in the context of stability. In particular, we are looking for the slowest decaying solution, that is maximal asymptotic. We present some new result on nonexistence of maximal asymptotics for certain
Piotr Polak, Grigory M. Sklyar
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Operator Multipliers Generating Strongly Continuous Semigroups

Semigroup Forum, 1997
Let \(X\) be a Banach space. Given a family of (not necessarily bounded) operators on \(X\), \(\{A(s):s\in\mathbb{R}\}\). We can define an operator \(\mathcal A\) on \(C_0(\mathbb{R},X)\) by \[ ({\mathcal A})(s)= A(s)f(s)\quad\text{for}\quad f\in D({\mathcal A})\quad\text{and} \quad s\in\mathbb{R}, \] for a suitable definition of the domain \(D ...
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Heat treatment modelling using strongly continuous semigroups

Computers in Biology and Medicine, 2015
In this paper, mathematical simulation of bioheat transfer phenomenon within the living tissue is studied using the thermal wave model. Three different sources that have therapeutic applications in laser surgery, cornea laser heating and cancer hyperthermia are used.
Alaeddin Malek, Ghasem Abbasi
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Invariant subsets of strongly continuous semigroups

Integral Equations and Operator Theory, 1984
Let A be the generator of a strongly continuous semigroup \(\{\) P(t): \(t\geq 0\}\) of continuous linear operators defined on a Banach space X. Let C be a \(\|.\|\)-closed convex subset of X and suppose that for every x in D(A) there exists a sequence \((x_ n: n\in ({\mathbb{N}}))\) in D(A) with the following properties: \(\lim \| x-x_ n\| =\lim \| Ax-
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ON THE SPECTRAL CHARACTERIZATION OF A STRONGLY CONTINUOUS PERTURBED SEMIGROUP

Acta Mathematica Scientia, 1995
Abstract In this paper, we get a sufficient condition to estimate the essential type of a strongly continuous semigroup in a Banach space, using this condition we prove that the essential type of the strongly continuous semigroup don't increase under the A – smoothing perturbation and establish the spectral mapping theorem for the asymptotic parts of
Haiyan Wang, Mingzhu Yang
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