Bases of Exponentials in Weighted Spaces Generated by Zeros of the Fourier–Stieltjes Transform

The system of exponentials generated by zeros of the Fourier–Stieltjes transform of a finite function with discontinuities at the ends of the support interval $[-a,a]$ is considered in the Lebesgue space on the interval $(-a,a)$ with weight in the form of a finite product of polynomial functions. A sufficient condition, which is unimprovable in a sense, is obtained for the basis property of such a system.