@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 estimates for the approximation numbers of composition operators on $H^2$, in terms of some modulus of continuity. For symbols whose image is contained in a polygon, we get that these approximation numbers are dominated by $\\e^{- c \\sqrt n}$. When the symbol is continuous on the closed unit disk and has a domain touching the boundary non-tangentially at a finite number of points, with a good behavior at the boundary around those points, we can improve this upper estimate. A lower estimate is given when this symbol has a good radial behavior at some point. As an application we get that, for the cusp map, the approximation numbers are equivalent, up to constants, to $\\e^{- c \\, n / \\log n }$, very near to the minimal value $\\e^{- c \\, n}$. We also see the limitations of our methods. To finish, we improve a result of O. El-Fallah, K. Kellay, M. Shabankhah and H. Youssfi, in showing that for every compact set $K$ of the unit circle $\\T$ with Lebesgue measure $0$, there exists a compact composition operator $C_\\phi \\colon H^2 \\to H^2$, which is in all Schatten classes, and such that $\\phi = 1$ on $K$ and $|\\phi | < 1$ outside $K$.
            """ ;
    dct:identifier "hal-00704746" ;
    dct:issued "2026-05-16T01:42:34.746208"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-16T01:42:34.746214"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Estimates for approximation numbers of some classes of composition operators on the Hardy space" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
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    dcat:keyword "approximation-numbers",
        "blaschke-product",
        "composition-operator",
        "cusp-map",
        "hardy-space",
        "infoeu-reposemanticspreprint",
        "mathmath-famathematics-mathfunctional-analysis-mathfa",
        "modulus-of-continuity",
        "msc-2010-primary-47b06----secondary-30j10--47b33",
        "preprints-working-papers-",
        "schatten-classes" ;
    dcat:landingPage <https://univ-artois.hal.science/hal-00704746> .

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    dct:issued "2026-05-16T01:42:34.851492"^^xsd:dateTime ;
    dct:modified "2026-05-16T01:42:34.714045"^^xsd:dateTime ;
    dct:title "Estimates for approximation numbers of some classes of composition operators on the Hardy space" ;
    dcat:accessURL <https://univ-artois.hal.science/hal-00704746> .

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