@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

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    dct:description """
              We give in this paper topological and dynamical characterizations of mathematical quasicrystals. Let U denote the space of uniformly discrete subsets of the Euclidean space. Let A denote the elements of U that admit an autocorrelation measure. A Patterson set is an element of A such that the Fourier transform of its autocorrelation measure is discrete. Patterson sets are mathematical idealizations of quasicrystals. We prove that S in A is a Patterson set if and only if S is almost periodic in (U,T), where T denotes the Besicovitch topology. Let chi be an ergodic random element of U. We prove that chi is almost surely a Patterson set if and only if the dynamical system has a discrete spectrum. As an illustration, we study deformed model sets.
            """ ;
    dct:identifier "hal-00078642" ;
    dct:issued "2026-05-14T14:38:42.335559"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-14T14:38:42.335565"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Quasicrystals and almost periodicity" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00078642v1/resource/17cab10f-f281-48e9-a2d3-8e85bf05d623> ;
    dcat:keyword "52c23-60g55",
        "almost-periodicity",
        "dynamical-system",
        "harmonic-analysis",
        "infoeu-reposemanticsarticle",
        "journal-articles",
        "mathmath-mpmathematics-mathmathematical-physics-math-ph",
        "mathmath-prmathematics-mathprobability-mathpr",
        "palm-measure",
        "quasicrystal",
        "spectral-measure",
        "stochastic-geometry" ;
    dcat:landingPage <ISSN:%200010-3616> .

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    dct:format "HTML" ;
    dct:issued "2026-05-14T14:38:42.339891"^^xsd:dateTime ;
    dct:modified "2026-05-14T14:38:42.305677"^^xsd:dateTime ;
    dct:title "Quasicrystals and almost periodicity" ;
    dcat:accessURL <https://hal.science/hal-00078642> .

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