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Related Experiment Video

Updated: Jun 28, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Computing with almost periodic functions.

R V Moody¹, M Nesterenko, J Patera

¹Department of Mathematics, University of Victoria, British Columbia, Canada. rmoody@uvic.ca

Acta Crystallographica. Section A, Foundations of Crystallography

|October 22, 2008

Summary

This study introduces a practical, group-theory based method for discrete Fourier analysis on quasicrystals. The approach provides uniform approximations for functions across infinite spaces, applicable to various quasicrystal models.

Related Experiment Videos

Last Updated: Jun 28, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Mathematical Physics
Harmonic Analysis
Materials Science

Background:

Quasicrystals and almost periodic sets exhibit complex structures challenging traditional Fourier analysis.
Existing methods often struggle with the non-periodic nature of these materials.
The emerging theory of quasicrystals and diffraction provides new frameworks for analysis.

Purpose of the Study:

To develop a discrete computational Fourier analysis method for functions on quasicrystals.
To leverage local hulls and dynamical systems within quasicrystal theory for diffraction analysis.
To create practical, computable approximations for functions on infinite quasicrystal structures.

Main Methods:

Utilizing group theory and finite group duals for a group-theoretical approach.
Building analysis around the Fourier module of the specific quasicrystal.
Employing local hulls and dynamical systems in the analysis framework.

Main Results:

Development of a novel discrete computational Fourier analysis method.
Achieving uniform approximations of target functions across the entire infinite space.
Demonstration of practical and computable group-theoretical methods.

Conclusions:

The developed method offers a robust way to perform Fourier analysis on quasicrystals.
The approach is applicable to all quasicrystals modeled using the cut-and-project formalism.
The group-theoretical foundation ensures practicality and computability for real-world applications.