# Periodic functions in dilations

1. Aug 31, 2011

### zetafunction

is it possible to find a function f different from $$f(x)=constant$$

with the property $$f(kx)=f(x)$$ for some real and positive 'k' ???

this is somehow 'dilation periodicity' is the equivalent to the periodic funciton $$f(x+k)=f(x)$$ for some positive 'k' for the traslation group

2. Aug 31, 2011

### tiny-tim

yes

try a substitution