Singular points of a self-similar function of spectral order zero: self-similar Stieltjes string
The author defines self-similar functions as fixed points for similarity operators. These operators are compositions of piecewise shifts, dilations and renormalizations. The spectral order of a function is defined in terms of the renormalization coefficients. Some basic properties of self-similar functions are studied: when are they piecewise constant, when are they non-decreasing.
scientific article; zbMATH DE number 5980669