Entire functions of Bernstein's class that are not Fourier–Stieltjes transforms

We consider certain subclasses of the class of entire functions of exponential type bounded on the real axis. We construct functions that belong to these subclasses but are not Fourier–Stieltjes transforms. Particular attention is given to the distribution of zeros of such functions. The results obtained allow us to study the stability of completeness of systems of exponentials in $C$ and $L_p$ under small perturbations of the exponents.