Positivity 8: 1–9, 2004. 1 © 2004 Kluwer Academic Publishers. Printed in the Netherlands. 1 1 1 SAID BOULITE , LAHCEN MANIAR , ABDELAZIZ RHANDI and JÜRGEN VOIGT Cadi Ayyad University, Faculty of Sciences Semlalia, B.P. 2390, Marrakesh, Morocco. E-mail: email@example.com, firstname.lastname@example.org, email@example.com Technische Universität Dresden, Fachrichtung Mathematik, D-01062 Dresden, Germany. E-mail: firstname.lastname@example.org (Received 28 November 2000; accepted 23 January 2003) Abstract. In this note we describe the generator of the modulus semigroup of the C -semigroup associated with the delay equation u t= Aut+Lu t0 u0= x∈Ru = f ∈ L −h0R 0 p n n in the Banach lattice R ×L −h0R . Mathematics Subject Classiﬁcation (2000): 34K06 Key words: functional differential equation, modulus semigroup, perturbation theory Dedicated to our friend Rainer Nagel on the occasion of his 60th birthday 1 Introduction The starting point of our considerations is the Cauchy problem for the linear delay equation u t= Aut+Lu t0 (DE) u0= x u =f n n in the L -context, for 1p<, with initial values x∈R , f ∈ L −h0R . p p n×n n n Here, h=1or h=, A= A ∈R , and LC−h0R →R is the ij bounded linear operator given by
Positivity – Springer Journals
Published: Oct 21, 2004
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