ON GENERATORS OF INTEGRATED C-SEMIGROUPS AND C-COSINE FUNCTIONS

The following two theorems are proved: (1) the generator of an exponentially equicontinuous n-times integrated C-cosine function also generates an exponentially equicontinuous [(n + 1)/2]-times integrated C-semigroup; (2) If A and -A are generators of exponentially equicontinuous n-times integrated C-semigroups, then A2 generates an exponentially equicontinuous n-times integrated C-cosine function.