| Résume | The talk is devoted to the study of exponential Riesz bases in $L^2(S)$, where $S$ is the union of multiple intervals. This problem is equivalent to describing complete interpolating sequences for the Paley-Wiener space $PW_S$.We begin by reviewing the classical characterization of exponential bases for a single interval due to Pavlov, Khrushchev, Nikolskii, and Minkin. Then, we discuss recent progress on the case where $S$ consists of multiple intervals. We finish by stating our recent results in the two interval case: sufficient conditions and close necessary conditions. In particular, we demonstrate an effect of an extra point in comparison with one interval of the same length. The talk is based on a joint work with Yu. Belov. |
