Replicative Functions

Author: Yoder, Michael Franz

Year: 1978

Degree: Dissertation (Ph.D.)

Advisor: Todd, John

Committee Member: Unknown, Unknown

Option: Mathematics

DOI: 10.7907/zdd8-gq82

Abstract

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.

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