On Independent and Stationary Subsystems of the Walsh System and Periodic Multiplicative Systems

V. F. Gaposhkin

Moscow State University of Railway Communications

Abstract: We show that the independence and stationarity properties in the narrow sense are equivalent for subsystems of the Walsh system. We consider several analogs of this result and some distinctions for subsystems of periodic multiplicative systems.

Keywords: Walsh system, periodic multiplicative system, weak multiplicativity, stationarity, boundary subsystem, Rademacher system.

UDC: 517.518.83

Received: 26.06.2008

DOI: 10.4213/mzm5163

 English version: Mathematical Notes, 2009, 85:3, 340–347

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