The excess of sets of complex exponentials

Abstract:

Let $\Lambda = \{ {\lambda _n}\}$ be a complex sequence and denote its associated set of complex exponentials $\{ \exp (i{\lambda _n}x)\}$ by $e(\Lambda )$. Redheffer and Alexander have shown that if $\sum {|{\lambda _n} - {\mu _n}|} < \infty$ then $e(\Lambda )$ and $e(\mu )$ have the same excess over their common completeness interval. This paper shows this result to be the best possible.