Spectral notions of aperiodic order
Copyright policy )Spectral notions of aperiodic order
Various spectral notions have been employed to grasp the structure of point sets, in particular non-periodic ones. In this article, we present them in a unified setting and explain the relations between them. For the sake of readability, we use Delone sets in Euclidean space as our main object class, and give generalisations in the form of further examples and remarks.
32 pages, with 2 figures; review-style article
- Bielefeld University Germany
Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc., Symbolic dynamics, Dynamical Systems (math.DS), spectrum, di ff raction versus dynamical, Mathematics - Spectral Theory, distributions and measures, Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups, Delone dynamical system, quasicrystal, dynamical spectrum, FOS: Mathematics, aperiodic order and quasicrystals, Quasicrystals and aperiodic tilings in discrete geometry, aperiodic order, Mathematics - Dynamical Systems, Spectral Theory (math.SP), Symbolic and Delone dynamical systems, 37-02, 43-01, 52C23
Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc., Symbolic dynamics, Dynamical Systems (math.DS), spectrum, di ff raction versus dynamical, Mathematics - Spectral Theory, distributions and measures, Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups, Delone dynamical system, quasicrystal, dynamical spectrum, FOS: Mathematics, aperiodic order and quasicrystals, Quasicrystals and aperiodic tilings in discrete geometry, aperiodic order, Mathematics - Dynamical Systems, Spectral Theory (math.SP), Symbolic and Delone dynamical systems, 37-02, 43-01, 52C23
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