A perturbation theorem for local C-regularized cosine functions

Motivated by the previous works on C-regularized semigroups and C-regularized cosine functions, this paper presents a new result concerning the multiplicative perturbation of local C-regularized cosine functions on a Banach space X. Two cases are considered: (1) the range of the regularizing operator C is not dense in X; (2) the operator C may not commute with the perturbation operator