On sums and products of periodic functions (Q1047476)

The authors study periodicity of sums of several periodic functions with common domain, and the product of two periodic functions with possibly different domains. Among various results, the authors show that for given continuous periodic functions \(f_1,f_2,\dots,f_n\), which are nonconstant on their common domain \(D\), if all the sums \(\sum_{i\in I}f_i\) are nonconstant, where \(I\subsetneq \{1,2,\dots,n\}\), then \(\sum_{1\leq i\leq n}f_i\) is periodic if and only if the periods of the summands are commensurable.