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[{"key": "dc.contributor.advisor", "value": "Onninen, Jani.", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Rasimus, Martti", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2015-08-17T11:19:55Z", "language": "", "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2015-08-17T11:19:55Z", "language": "", "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2015", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1492842", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/46630", "language": "", "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4m\u00e4n tutkielman tarkoituksena on tarkastella \u00e4\u00e4rellisen v\u00e4\u00e4nn\u00f6n\r\nkuvauksia euklidisissa avaruuksissa, erityisesti niiden diskreettisyytt\u00e4\r\nja avoimuutta. \u00c4\u00e4rellisen v\u00e4\u00e4nn\u00f6n kuvaukset ovat yleistys kvasis\u00e4\u00e4nn\u00f6llisist\u00e4\r\nkuvauksista, jotka molemmat m\u00e4\u00e4ritell\u00e4\u00e4n k\u00e4ytt\u00e4m\u00e4ll\u00e4 v\u00e4\u00e4nt\u00f6ep\u00e4yht\u00e4l\u00f6\u00e4.\r\nKvasis\u00e4\u00e4nn\u00f6llisille eli rajoitetun v\u00e4\u00e4nn\u00f6n kuvauksille voimassa olevat\r\ntulokset jatkuvuudesta, diskreettisyydest\u00e4 ja avoimuudesta s\u00e4ilyv\u00e4t\r\nmy\u00f6s \u00e4\u00e4relliseen v\u00e4\u00e4nt\u00f6\u00f6n siirrytt\u00e4ess\u00e4. T\u00e4h\u00e4n tarvitaan kuitenkin joitain\r\noletuksia kuvauksen v\u00e4\u00e4nt\u00f6funktiosta. Ty\u00f6ss\u00e4 konstruoidaan vastaesimerkkej\u00e4\r\nkuvauksista, joille n\u00e4m\u00e4 ominaisuudet eiv\u00e4t v\u00e4ltt\u00e4m\u00e4tt\u00e4\r\nole voimassa.\r\nTutkielman p\u00e4\u00e4tuloksina osoitetaan, ett\u00e4 Sobolev-avaruuden W^(1,n)_loc\r\n\u00e4\u00e4rellisen v\u00e4\u00e4nn\u00f6n kuvauksella on olemassa jatkuva edustaja, joka on\r\nvakio tai diskreetti ja avoin, kun oletetaan lis\u00e4ksi, ett\u00e4 v\u00e4\u00e4nt\u00f6funktio K on kyllin integroituva. N\u00e4iden tulosten\r\nrinnalla todistetaan molempien v\u00e4itteiden seuraavan vaihtoehtoisesti\r\nmy\u00f6s siit\u00e4, ett\u00e4 v\u00e4\u00e4nt\u00f6funktio on eksponentiaalisesti integroituva.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Martti Rasimus (mailrasi) on 2015-08-17 11:19:54.832877. Form: Pro gradu -lomake (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake). JyX data: [jyx_publishing-allowed (fi) =True]", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija.group@korppi.jyu.fi) on 2015-08-17T11:19:55Z\r\nNo. of bitstreams: 2\r\nURN:NBN:fi:jyu-201508172680.pdf: 632584 bytes, checksum: 25849b0dbc8bffdf1967c9683fbcf1fa (MD5)\r\nlicense.html: 4819 bytes, checksum: 49dd5315dc20dc46754282ecea992ac3 (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2015-08-17T11:19:55Z (GMT). No. of bitstreams: 2\r\nURN:NBN:fi:jyu-201508172680.pdf: 632584 bytes, checksum: 25849b0dbc8bffdf1967c9683fbcf1fa (MD5)\r\nlicense.html: 4819 bytes, checksum: 49dd5315dc20dc46754282ecea992ac3 (MD5)\r\n Previous issue date: 2015", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto (69 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": "\u00c4\u00e4rellinen v\u00e4\u00e4nt\u00f6", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "jatkuvuus", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "diskreettisyys", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "avoimuus", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "distributiivinen Jacobi", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "heikko monotonisuus", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "topologinen aste", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "\u00c4\u00e4rellisen v\u00e4\u00e4nn\u00f6n kuvaukset : diskreettisyys ja avoimuus", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": 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