Взаємозв'язки двосимвольного та чотирисимвольного $Q$-зображень дробової частини дійсного числа

Abstract

We consider a $Q_2$-representation of a fractional part of a real
number. This is a one-parameter generalization of a classic binary
representation. For a given $Q_2$-expansion and corresponding
representation, induced four-symbol $Q_4$-representation is
introduced. The conditions when the four-symbol $Q_4$-representation is
induced by a two-symbol representation as well as the conditions for
the two-symbol conversion of the four-symbol $Q_4$-representation to be
a $Q_2$-representation are found. A class of singular functions is
constructed by simple conversion of a four-symbol $Q_4$-representation
to a two-symbol $Q_2$-representation.