The Adjoint of a Semigroup of Linear Operators

1992 ◽  
Author(s):  
Jan van Neerven
Keyword(s):  
Linear Operators ◽  
Semigroup Of Linear Operators

scholarly journals Necessary conditions of optimality for infinite dimensional uncertain systems

1995 ◽  
Vol 1 (3) ◽  
pp. 179-191 ◽  
Author(s):  
N. U. Ahmed ◽  
X. Xiang
Keyword(s):  
Uncertain Systems ◽  
Infinitesimal Generator ◽  
Continuous Semigroup ◽  
Computational Algorithm ◽  
Necessary Conditions ◽  
Reflexive Banach Space ◽  
Linear Operators ◽  
Infinite Dimensional ◽  
Necessary Conditions Of Optimality ◽  
Semigroup Of Linear Operators

In this paper we consider optimal control problem for infinite dimensional uncertain systems. Necessary conditions of optimality are presented under the assumption that the principal operator is the infinitesimal generator of a strongly continuous semigroup of linear operators in a reflexive Banach space. Further, a computational algorithm suitable for computing the optimal policies is also given.

scholarly journals On the asymptotic behaviour of a semigroup of linear operators

1995 ◽  
Vol 6 (4) ◽  
pp. 453-476 ◽  
Author(s):  
J.M.A.M. van Neerven ◽  
B. Straub ◽  
L. Weis
Keyword(s):  
Asymptotic Behaviour ◽  
Linear Operators ◽  
Semigroup Of Linear Operators

scholarly journals C0-continuity of the Fröbenius-Perron semigroup

2002 ◽  
Vol 31 (5) ◽  
pp. 307-319
Author(s):  
Andrés Navas ◽  
Sergio Plaza
Keyword(s):  
Invariant Measure ◽  
Topological Space ◽  
Linear Operators ◽  
Regular Measure ◽  
Geometrical Condition ◽  
Semidynamical System ◽  
Semigroup Of Linear Operators

We consider the Fröbenius-Perron semigroup of linear operators associated to a semidynamical system defined in a topological spaceXendowed with a finite or aσ-finite regular measure. We prove that if there exists afaithful invariant measurefor the semidynamical system, then the Fröbenius-Perron semigroup of linear operators isC0-continuous in the spaceLμ 1(X). We also give a geometrical condition which ensuresC0-continuity of the Fröbenius-Perron semigroup of linear operators in the spaceLμ p(X)for1≤p<∞, as well as in the spaceLloc 1.

scholarly journals Scaling limits of solutions of linear evolution equations with random initial conditions

2017 ◽  
Vol 17 (03) ◽  
pp. 1750019 ◽  
Author(s):  
Miłosz Krupski
Keyword(s):  
Evolution Equations ◽  
Initial Conditions ◽  
Linear Operators ◽  
Scaling Limits ◽  
Initial Value ◽  
Linear Evolution ◽  
Semigroup Of Linear Operators ◽  
Random Initial Conditions ◽  
Stationary Random Field ◽  
Linear Evolution Equations

We consider a linear equation [Formula: see text], where [Formula: see text] is a generator of a semigroup of linear operators on a certain Hilbert space related to an initial condition [Formula: see text] being a generalised stationary random field on [Formula: see text]. We show the existence and uniqueness of generalised solutions to such initial value problems. Then we investigate their scaling limits.

Semigroups of Operators in C(S)

1970 ◽  
Vol 22 (1) ◽  
pp. 47-54 ◽  
Author(s):  
F. Dennis Sentilles
Keyword(s):  
Transition Function ◽  
Continuous Functions ◽  
Linear Operators ◽  
Semigroups Of Operators ◽  
Supremum Norm ◽  
Strict Topology ◽  
Borel Measures ◽  
Transition Functions ◽  
Semigroup Of Linear Operators ◽  
Bounded Continuous Functions

Our study in this paper is two-fold: One is that of a semigroup of linear operators on the space C(S) of bounded continuous functions on a locally compact Hausdorff space S, while the other is that of a transition function of measures in the Banach space M(S) of bounded regular Borel measures on S. It will be seen that an informative and essentially non-restrictive theory of the former can be obtained when C(S) is given the strict topology rather than the usual supremum norm topology and that, in this setting, the natural relationship between semigroups and transition functions obtained when S is compact is maintained, essentially because the dual of C(S) with the strict topology is M(S).

scholarly journals Vector valued ergodic theorems for a one-parameter semigroup of linear operators

1978 ◽  
Vol 30 (1) ◽  
pp. 95-106 ◽  
Author(s):  
Shigeru Hasegawa ◽  
Ryōtarō Satō ◽  
Shigeru Tsurumi
Keyword(s):  
Linear Operators ◽  
Ergodic Theorems ◽  
Semigroup Of Linear Operators ◽  
Vector Valued
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