Fourier indices of an almost-periodic function

The real numbers in the Fourier series corresponding to the given almost-periodic function :

where the are the Fourier coefficients of (cf. Fourier coefficients of an almost-periodic function; Fourier series of an almost-periodic function). The set of Fourier indices of a function is called its spectrum. In contrast to the periodic case, the spectrum of an almost-periodic function can have finite limit points and can even be everywhere dense. Therefore, the behaviour of the Fourier series of an almost-periodic function depends in an essential way on the arithmetic structure of its spectrum.