ON ONE SPECTRUM OF UNIVERSALITY FOR WALSH SYSTEM

Abstract

In the present work it is shown that the set $D=\{\sum \limits^{\infty}_{i=o}\delta_i2^{N_i} : \delta_i=0,~1\},$ for every sequence $N_0 < N_1 <…< N_i <… $ of natural numbers can be changed into the set of the form $\Lambda = \{k + o(\omega(k)) : k \in D\},$ where $\omega(k)$ is an arbitrary, tending to infinity at $k\rightarrow\infty$ sequence, such that $\Lambda$ is the spectrum of universality for Walsh system.