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Norm Inequalities for Generators of Analytic Semigroups and Cosine Operator Functions

Published online by Cambridge University Press:  20 November 2018

Jamil A. Siddiqi  and
Abdelkader Elkoutri
Jamil A. Siddiqi
Affiliation:
Département de mathématiques, statistique et actuariat, Université Laval, Québec, Canada G1K 7P4
Abdelkader Elkoutri
Affiliation:
Département de mathématiques, Faculté des sciences de Marrakech, Marrakech, Maroc
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Abstract

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We prove that if A is the infinitesimal generator of a bounded analytic semigroup in a sector {z ∊ C : |arg z| ≦ (απ)/2} of bounded linear operators on a Banach space, then the following inequalities hold:

for any x ∊ D(An) and for any 0 < β < α. This result helps us to answer in affirmative a question raised by M. W. Certain and T. G. Kurtz [3]. Similar inequalities are proved for cosine operator funtions.

Keywords

Norm inequalitiesanalytic semigroup of operatorsinfinitesimal generatorcosine operator function
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 1 , 01 March 1989 , pp. 47 - 53
Copyright
Copyright © Canadian Mathematical Society 1989

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