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International Journal of Mathematics and Mathematical Sciences
Volume 19, Issue 3, Pages 575-580

Integrated cosine functions

Dept. of Math., Huazhog Univ. of Science and Technology, Wuhan 430074, China

Received 18 June 1993; Revised 20 June 1994

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In order to the second order Cauchy problem (CP2):x(t)=Ax(t), x(0)=xD(An), x(0)=yD(Am) on a Banach space, Arendt and Kellermann recently introduced the integrated cosine function. This paper is concerned with its basic theory, which contain some properties, perturbation and approximation theorems, the relationship to analytic integrated semigroups, interpolation and extrapolation theorems.