Biorthogonal systems for exponential systems on a disconnected set

We study the properties of a system biorthogonal to a complete and minimal system of exponentials in $L^2(E)$, where $E$ is a finite union of intervals, and show that in the case when $E$ is a union of two or three intervals the biorthogonal system is also complete. This result generalizes the well-known R. Yang theorem for the case of one interval. The report is based on joint work with Yu. Belov and A. Kuznetsov.