English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Primitive inflation tilings of the real line with finitely many tiles ofnatural length and a Pisot--Vijayaraghavan unit as inflation factor areconsidered. We present an approach to the pure point part of their diffractionspectrum on the basis of a Fourier matrix cocycle in internal space. Thiscocycle leads to a transfer matrix equation and thus to a closed expression ofmatrix Riesz product type for the Fourier transforms of the windows for thecovering model sets. In general, these windows are complicated Rauzy fractalsand thus difficult to handle. Equivalently, this approach permits aconstruction of the (always continuously representable) eigenfunctions for thetranslation dynamical system induced by the inflation rule. We review andfurther develop the underlying theory, and illustrate it with the family ofPisa substitutions, with special emphasis on the Tribonacci case.

Fourier transform of Rauzy fractals and point spectrum of 1D Pisot inflation tilings