Pure discrete spectrum in substitution tiling spaces

TL;DR

This paper presents a new method to determine when substitution tiling systems of Pisot family type have pure discrete spectrum, supported by multiple illustrative examples.

Contribution

It introduces a novel procedure for establishing pure discrete spectrum in substitution tiling systems of Pisot family type.

Findings

Procedure successfully applied to several examples

Provides a systematic way to verify pure discrete spectrum

Enhances understanding of spectral properties in tiling spaces

Abstract

We introduce a procedure for establishing pure discrete spectrum for substitution tiling systems of Pisot family type and illustrate with several examples.