Matrices of operators and regularized cosine functions

This paper is concerned with matrices of abstract differential operators which are parabolic in the sense of Shilov or correct in the sense of Petrovskij.We show that they generate regularized cosine functions with suitable regularizing operators under sharper conditions. The results then are applied to matrices of partial differential operators on many function spaces. Finally, the wellposedness of the associated second-order systems is discussed.  2005 Elsevier Inc. All rights reserved