Functional Equations, D'Alembert Functions, Abelian
This major paper is devoted to the study of pre-d'Alembert functions and d'Alembert functions on groups.
In this paper, we first study additive and multiplicative Cauchy equations and the sine addition formula on groups. Then we discuss some properties ofpre-d'Alembert functions on groups. In particular, we characterize when a pre-d'Alembert function is abelian, and furthermore get the general form of abelian pre-d'Alembert functions on groups. Finally we achieve our goal: we obtain the structure of the solution by group representation theory.
Master of Science
Mathematics and Statistics
Major Research Paper