Substitution-based sequences with absolutely continuous diffraction

TL;DR

This paper introduces a new substitution-based sequence derived from Rudin's construction, which exhibits a purely absolutely continuous diffraction spectrum, advancing understanding of diffraction properties in mathematical sequences.

Contribution

It presents a novel substitution sequence with absolutely continuous diffraction spectrum, extending Rudin-Shapiro sequence analysis.

Findings

Sequence has purely absolutely continuous diffraction spectrum

Extends Rudin-Shapiro sequence analysis

Provides new examples in diffraction theory

Abstract

Modifying Rudin's original construction of the Rudin-Shapiro sequence, we derive a new substitution-based sequence with purely absolutely continuous diffraction spectrum.