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On sums and products of periodic functions. (English) Zbl 1185.26001

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.

MSC:

26A06 One-variable calculus
26A99 Functions of one variable
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