The singular points of self-similar functions with zero spectral degree. Stieltjes self-similar string

TL;DR

This paper investigates the singular points of self-similar functions with zero spectral degree, providing a complete classification and exploring their connection to spectral problems like the Stieltjes string.

Contribution

It introduces a classification of singular points for zero spectral degree self-similar functions and links these functions to spectral problems such as the Stieltjes string.

Findings

Complete classification of singular points in zero spectral degree self-similar functions

Establishment of a connection between these functions and spectral problems

Insights into the structure of Stieltjes self-similar strings

Abstract

The self-similar functions of zero spectral degree are defined. The singular points of these functions are investigated and full classification of points is given. The connection with spectral problems (Stieltjes string) is pointed out.