Abstract: In this paper, we study the interpolation and extrapolation theorems of regularized cosine operator funcitons. We show that the linear Operator a generates a exponentially bounded C -regularized cosine function on the Banach space X if and only if there exist a Banach space Y and a linear operator B such that:[R(C]→x→y, where C is a bounded extension of C on Y, B generates a strongly continuous cosine operator funciton and A=B|_x.

Key words: Regularized cosine function, Integrated cosine funcitons, Interpolation and extrapolation