Replicative Functions

Functions are considered which satisfy the set of equations [see PDF abstract for equation] for given sequences {an}, {bn}.· In the first part of the dissertation f is assumed to be a continuous function from the real line to the complex plane; the cases where f is periodic and aperiodic are considered separately. All possible aperiodic functions are determined; for f periodic the Fourier series is determined. Some miscellaneous results are also given. In the second part f is considered to be a function from the complex plane to itself which is holomorphic except at isolated points. Again the cases where f is periodic and aperiodic are considered separately, and all possible fare determined for both cases.