The Modulus Semigroup for Linear Delay Equations

Abstract

Abstract. In this note, we describe the generator of the modulus semigroup of the C 0 -semigroup associated with the delay equation

Modulus Semigroups and Perturbation Classes for Linear Delay Equations in Lp

“…Then we determine the modulus semigroup in a rather general context. This generalises the results of [5], [13], [10].…”

The modulus semigroup for linear delay equations III

“…This result is shown in [3] for the case X = R n , where necessarily the generator A is a bounded operator. In [11] the result is generalised to the case of a Banach lattice X with order continuous norm, but still with a bounded generator A.…”

“…In the present paper the results of the papers [3,11] are further generalised. The main object is to obtain the modulus semigroup for a C 0 -semigroup arising in the study of the initial value problem for a linear differential equation with delay,…”

A note on a criterion for M-matrix

“…Based on the properties of an M -matrix, some stability criterions of a certain class of functional differential equation have been provided in [1][2][3][4][5][6]. The control problem of such a dynamical system can be reduced to finding a variable transformation such that the transformed system satisfies the stability condition with an M -matrix [7].…”