A necessary condition for the uniform minimality of a system of exponentials in L-P spaces on the lineстатья
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Аннотация:A necessary condition for the uniform minimality of a system of weighted exponentials exp(-ilambda(n)t - a\t\(alpha)), a > 0, alpha > 1, is obtained in the spaces L-p (1 less than or equal to p < infinity) and C-0 on the real line and the half-line. This condition is stated in terms of the indicator of the entire function of order beta = alpha/(alpha - 1) with zero set coinciding with the sequence lambda(n). This condition is used to show that there are no bases among the known complete minimal systems of this form in the above-indicated spaces.