A criterion of unconditional basis property for the families of vector exponentials (Q2255711)

The authors consider the family of functions \(E_{n}(t):=c_{n}e^{i\lambda_{n}t}\), \(\lambda_{n}\in \Lambda\), where \(c_{n}\) are constant vectors from \(C^{m}\) and \(\Lambda=\{\lambda_{k}\}_{-\infty}^{+\infty}\) is a complex sequence with the single limiting point \(\infty\). They prove a criterion of unconditional basis property for the above families in \(L_{2}^{(n)}(0,a)\) (the Cartesian product of \(n\) spaces \(L_{2}(0,a)\) with the standard scalar product) without the strong restriction: \(\inf \operatorname{Im}\lambda_{n}>-\infty\), \(\lambda_{n}\in \Lambda\).