  We consider the problem of determining the Fourier integral in the Hilbert
space of square integrable functions. Fourier integral is the scalar product of
two functions belonging to the Hilbert space of square integrable functions and
the Hilbert space of almost periodic functions. Scalar product for different
Hilbert spaces defined at the intersection of these spaces, which contains only
one zero element. Therefore, the Fourier integral is not defined in the Hilbert
space of square integrable functions with nonzero norm.
