Exponential bases for partitions of intervals

For a partition of [0, 1] into intervals ������1, ... , ������������we prove the existence of a partition of Z into Lambda 1, ... ,Lambda ������such that the complex exponential functions with frequencies in Lambda ������form a Riesz basis for ������2(������������), and furthermore, that for any ������ subset of {1, 2, ... , ������}, the exponential functions with frequencies in & Union;������is an element of ������Lambda ������form a Riesz basis for ������2(������)for any interval ������with length |������|= n-ary sumation ������is an element of ������|������������|. The construction extends to infinite partitions of [0, 1], but with size limitations on the subsets ������ subset of Z; it combines the ergodic properties of subsequences of Z known as Beatty-Fraenkel sequences with a theorem of Avdonin on exponential Riesz bases.