An Example Related to the Sidon Property for $m$-Dependent Systems

V. F. Gaposhkin^a, Yu. S. Semenov

^a Moscow State University of Railway Communications

Abstract: We establish a sufficient condition for an $m$-dependent system to be a Sidon system. It is proved that this condition cannot be strengthened for any natural $m$. The proof is based on the consistency of a certain system of quadratic equations over the field $\mathbb{R}$.

Keywords: $m$-dependent system, Sidon property, Sidon system, quadratic equation, random variable, Laurent polynomial, Rademacher system.

UDC: 519.2

Received: 26.06.2009

DOI: 10.4213/mzm8637

 English version: Mathematical Notes, 2011, 89:3, 336–339

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