International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1996 / Article

Open Access

Volume 19 |Article ID 518463 | https://doi.org/10.1155/S0161171296000798

Quan Zheng, "Integrated cosine functions", International Journal of Mathematics and Mathematical Sciences, vol. 19, Article ID 518463, 6 pages, 1996. https://doi.org/10.1155/S0161171296000798

Integrated cosine functions

Received18 Jun 1993
Revised20 Jun 1994

Abstract

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.

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.


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