In this paper we extend the area of applications of
the Abstract Harmonic Analysis to the field of Boolean function complexity.
In particular, we extend the class of functions to which
a spectral technique developed in a series of works of the first author
can be applied.
This extension allows us to prove that testing square-free numbers by
unbounded fan-in circuits of bounded depth requires a superpolynomial size.
This implies the same estimate for the integer factorization problem.