2002/12/03 by Jean-Baptiste Gouéré, Jean-Baptiste Gouere, Gouere, Jean-Baptiste · 2 citations
Earth and Planetary Sciences · Materials Science · Mathematics · Physics and Astronomy · #52C23 #60G55 #Analytic and geometric function theory #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mineralogy and Gemology Studies #Probability (math.PR) #Quasicrystal Structures and Properties #math-ph #math.MP #math.PR #msc:52C23 #msc:60G55
paper · pdf · doi:10.48550/arxiv.math-ph/0212012
arxiv created 2002/12/03 · openalex publication_date 2002/12/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a topology \cal T on the space U of uniformly discrete subsets of the Euclidean space. Assume that S in U admits a unique autocorrelation measure. The diffraction measure of S is purely atomic if and only if S is almost periodic in (U,\cal T). This result relates idealized quasicrystals to almost periodicity. In the context of ergodic point processes, the autocorrelation measure is known to exist. Then, the diffraction measure is purely atomic if and only if the dynamical system has a pure point spectrum. As an illustration, we study deformed model sets.