@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#> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-tel-00681558v1> a dcat:Dataset ;
    dct:description """
              Let L(X) be the algebra of all bounded operators on a Banach space X, and let t:G⇾L(X) be a representation of a topological group G in X. For every element g in the group G, we consider the projection on the unit circle T of the spectrum s(t(g)) of the invertible operator t(g), so we set s1(t(g)):={l/|l|, l∊s(t(g))}, and we consider the set S of all elements g in the group G such that s1(t(g)) does not contain any regular polygon of T, so we set S:={g∊ G / ∄ P∊P' / P ⊆ s1(t(g))}, where P' denotes the set of regular polygons of T (we call regular polygon in T the image by a rotation of a closed subgroup of T different from {1}). In the first part, we set out the principal results and notations subsequently used. When G is a locally compact abelian group, we prove in the second part that t is uniformly continuous if and only if t is measurable (L(X) is equipped with the norm topology) and if more G is second countable and t strongly continuous, we state in the third part that t is uniformly continuous if and only if S is non meager. In the same way, we show that t is uniformly continuous if and only if S is a non null set for the Haar measure on G. When G is a locally compact group and t a unitary representation of G in a Hilbert space H, we show also in the second part that t is uniformly continuous if and only if t is measurable, and if more G is metrizable and t strongly continuous, we prove in the third part that t is uniformly continuous if and only if {g∊ G / 0∉ Conv(s(t(g)))} is non meager, where Conv(S) denotes the convex hull of any subset S in a vector space.
            """ ;
    dct:identifier "tel-00681558" ;
    dct:issued "2026-05-23T20:06:21.625211"^^xsd:dateTime ;
    dct:language "fr" ;
    dct:modified "2026-05-23T20:06:21.625226"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Continuity of representations of topological groups" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-tel-00681558v1/resource/fb7330c7-0451-4611-a63b-1090c7114211> ;
    dcat:keyword "algebre-de-banach",
        "banach-algebra",
        "continuite",
        "continuity",
        "espace-de-hilbert",
        "hilbert-space",
        "infoeu-reposemanticsdoctoralthesis",
        "mathmath-famathematics-mathfunctional-analysis-mathfa",
        "measurability",
        "mesurabilite",
        "representation-de-groupe",
        "representation-of-group",
        "spectre",
        "spectrum",
        "theses" ;
    dcat:landingPage <https://theses.hal.science/tel-00681558> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-tel-00681558v1/resource/fb7330c7-0451-4611-a63b-1090c7114211> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-23T20:06:21.663721"^^xsd:dateTime ;
    dct:modified "2026-05-23T20:06:21.557690"^^xsd:dateTime ;
    dct:title "Continuity of representations of topological groups" ;
    dcat:accessURL <https://theses.hal.science/tel-00681558> .

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    foaf:name "test_moissonnage_selune" .

<https://theses.hal.science/tel-00681558> a foaf:Document .