| fullrecord |
[{"key": "dc.contributor.advisor", "value": "Kilpel\u00e4inen, Tero", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Koskelo, Reetta", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2024-08-06T05:19:33Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2024-08-06T05:19:33Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2024", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/96519", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 tutkielmassa osoitetaan p\u00e4\u00e4tuloksina Koeben 1/4-lause sek\u00e4 Haymanin-Wun lause. Koeben 1/4 -lause kertoo, ett\u00e4 analyyttinen injektio f ei voi kutistaa yksikk\u00f6kiekkoa D pienemm\u00e4ksi kuin yhteen nelj\u00e4sosaan alkuper\u00e4isest\u00e4, kun funktio f h\u00e4vi\u00e4\u00e4 origossa ja derivaatan arvo origossa on 1. Haymanin-Wun lause puolestaan antaa k\u00e4yr\u00e4n \u03c6-1(\u2126 \u2229 L) pituudelle yl\u00e4rajan 4\u03c0, kun \u2126 on yhdesti yhten\u00e4inen kompleksitason alue, L on mielivaltainen aluetta \u2126 leikkaava suora ja \u03c6 on konformikuvaus yksikk\u00f6kiekolta D alueelle \u2126. Tutkielmassa esitell\u00e4\u00e4n aluksi hy\u00f6dyllisi\u00e4 aputuloksia sek\u00e4 m\u00e4\u00e4ritelmi\u00e4, joita tarvtaan my\u00f6hemmin toisten tulosten todistamiseksi. Osalle n\u00e4ist\u00e4 aputuloksista esitell\u00e4\u00e4n my\u00f6s todistukset. Tutkielman teorian pohjalla on t\u00e4rke\u00e4ss\u00e4 roolissa konformikuvaukset, joten niihin tutustutaan aputulosten j\u00e4lkeen ensimm\u00e4iseksi. Konformikuvauksista tarkastellaan esityisesti M\u00f6bius-kuvauksia, jotka ovat hy\u00f6dyllinen konformikuvausten kategoria, mink\u00e4 j\u00e4lkeen esitell\u00e4\u00e4n kaksoissuhde sek\u00e4 M\u00f6bius-kuvausten l\u00f6yt\u00e4minen sen avulla. Lis\u00e4ksi todistetaan keskeinen konformikuvauksiin liittyv\u00e4 tulos Riemannin kuvauslause, jonka nojalla mielivaltaiselta kompleksitason yhdesti yhten\u00e4iselt\u00e4 alueelta on olemassa konformikuvaus yksikk\u00f6kiekolle D. Haymanin-Wun lauseen todistuksessa k\u00e4ytet\u00e4\u00e4n apuna hyperbolista ja pseudohyperbolista metriikkaa yksikk\u00f6kiekossa D sek\u00e4 harmonisen mitan ominaisuuksia. N\u00e4ist\u00e4 esitell\u00e4\u00e4n perusominaisuuksia sek\u00e4 todistuksille tarpeelliset tulokset. Lis\u00e4ksi osoitetaan Schwarzin lemma sek\u00e4 Schwarzin-Pickin lause. Koeben 1/4-lauseen todistus puolestaan pohjaa konformiseen moduliin sek\u00e4 sen ominaisuuksiin, erityisesti Gr\u00f6tzschin lauseeseen sek\u00e4 polkuperheiden konformiseen moduliin annuluksessa. Tutkielmassa tarkastellaan my\u00f6s kahdesti yhten\u00e4isi\u00e4 alueita sek\u00e4 niiden v\u00e4lisi\u00e4 konformikuvauksia.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2024-08-06T05:19:32Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2024-08-06T05:19:33Z (GMT). No. of bitstreams: 0\n Previous issue date: 2024", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "70", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "Koeben 1/4-lause", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Haymanin-Wun lause", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "konformikuvaukset", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "M\u00f6bius-kuvaukset", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Riemannin kuvauslause", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Schwarzin lemma", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "konforminen moduli", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Koeben 1/4-lause ja Haymanin-Wun lause", "language": "", "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202408065402", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "kompleksiluvut", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}]
|