| fullrecord |
[{"key": "dc.contributor.author", "value": "Hakavuori, Eero", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2014-06-23T09:10:17Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2014-06-23T09:10:17Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2014", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1437945", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/43818", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4m\u00e4n tutkielman tavoitteena on esitt\u00e4\u00e4, miten analyyttisen funktion m\u00e4\u00e4rittelyjoukko laajennetaan Riemannin pinnaksi, joka sis\u00e4lt\u00e4\u00e4 informaation kaikista funktion analyyttisist\u00e4 jatkeista kompleksitasossa. T\u00e4t\u00e4 Riemannin pintaa sanotaan kyseisen analyyttisen funktion Riemannin pinnaksi. Konstruktiota varten t\u00e4ytyy ensin tarkastella analyyttisen jatkeen k\u00e4ytt\u00e4ytymist\u00e4 kompleksitasossa, Riemannin pintojen ja kompleksitason v\u00e4list\u00e4 yhteytt\u00e4 sek\u00e4 perusryhm\u00e4n ja peitteiden k\u00e4ytt\u00e4ytymist\u00e4 Riemannin pintojen kontekstissa. Erityisesti tarkastellaan miten useat kompleksianalyysin perustulokset yleistyv\u00e4t suoraan Riemannin pinnoille ja Riemannin pintojen analyyttisille funktioille sek\u00e4 sit\u00e4, milloin Riemannin pinnan lokaali homeomorfismi on peite.\n\nT\u00e4rkeimpi\u00e4 tarkasteltavia funktioita tutkielmassa ovat juurifunktiot ja logaritmi. Osoittautuu, ett\u00e4 n\u00e4iden funktioiden analyyttisen jatkeen k\u00e4ytt\u00e4ytyminen punkteeratussa kiekossa karakterisoi kaikkien punkteeratussa kiekossa vapaasti jatkettavien analyyttisten funktioiden k\u00e4ytt\u00e4ytymisen. Erityisesti juurifunktion k\u00e4ytt\u00e4ytymisen tunteminen antaa tavan k\u00e4sitell\u00e4 analyyttisen funktion Riemannin pinnan muodostamiseen tarvittavia haarautumispisteit\u00e4. Lis\u00e4ksi tarkastellaan algebrallisten funktioiden analyyttisen jatkeen k\u00e4ytt\u00e4ytymist\u00e4 ja sit\u00e4, miten algebrallisen funktion Riemannin pinnan konstruktiota voidaan soveltaa algebrallisten k\u00e4yrien tarkasteluun.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Eero Hakavuori (eejohaka) on 2014-06-23 09:10:17.179947. Form: Pro gradu -lomake (1 tekij\u00e4) (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake-1-tekijae). JyX data:", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija@noreply.fi) on 2014-06-23T09:10:17Z\nNo. of bitstreams: 2\nURN:NBN:fi:jyu-201406232121.pdf: 921497 bytes, checksum: 0f2611175ce8cea178153a48e362418b (MD5)\nlicense.html: 4876 bytes, checksum: 934b89bb4c8934ba920e208893a2e003 (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2014-06-23T09:10:17Z (GMT). No. of bitstreams: 2\nURN:NBN:fi:jyu-201406232121.pdf: 921497 bytes, checksum: 0f2611175ce8cea178153a48e362418b (MD5)\nlicense.html: 4876 bytes, checksum: 934b89bb4c8934ba920e208893a2e003 (MD5)\n Previous issue date: 2014", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto (75 sivua)", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "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": "Riemannin pinnat", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "analyyttinen jatke", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "perusryhm\u00e4", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "peitteet", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "algebralliset funktiot", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "algebralliset k\u00e4yr\u00e4t", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Analyyttinen jatke ja Riemannin pinnat", "language": null, "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-201406232121", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "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": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "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": "dc.date.updated", "value": "2014-06-23T09:10:18Z", "language": null, "element": "date", "qualifier": "updated", "schema": "dc"}, {"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": "fi", "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": null, "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "funktiot", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "analyyttiset funktiot", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
|