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[{"key": "dc.contributor.author", "value": "Niinikoski, Joonas", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2016-09-27T16:58:19Z", "language": "", "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2016-09-27T16:58:19Z", "language": "", "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2016", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1574712", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/51469", "language": "", "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Tutkielmassa esitell\u00e4\u00e4n euklidisen avaruuden \u00e4\u00e4rellisille Borel-mitoille Fourier-muunnokset kompleksiarvoisina kuvauksina ja tutkitaan niiden v\u00e4henemist\u00e4 ment\u00e4ess\u00e4 \u00e4\u00e4arett\u00f6m\u00e4n kauas origosta. Keskeisen\u00e4 kysymyksen\u00e4 on, mill\u00e4 reunaehdoilla annetun kompkatikantajaisen ja \u00e4\u00e4rellisen Borel-mitan Fourier muunnos v\u00e4henee polynomiaalisesti (eli sit\u00e4 voidaan dominoida jollain euklidisen normin negatiivisella potenssilla) kaikkialla riitt\u00e4v\u00e4n kaukana tai ainakin \u201dkeskim\u00e4\u00e4r\u00e4isesti\u201d. Mik\u00e4li t\u00e4llainen Borel-mitta on\r\nabsoluuttisesti jatkuva Lebesguen mitan suhteen kompaktikantajaisella ja sile\u00e4ll\u00e4 tiheysfunktiolla, niin\r\nsen Fourier-muunnos v\u00e4henee aina polynomiaalisesti kaikkialla.\r\n\r\n\r\nOngelmaa tarkastellaan keskeisesti potentiaaliteorian avulla. Jokaiselle \u00e4\u00e4relliselle ja kompaktikantajaiselle Borel-mitalle asetetaan Rieszin energia. T\u00e4ll\u00f6in Rieszin energian \u00e4\u00e4rellisyys implikoi mitan Fourier-muunnoksen\r\npolynomiaalisen v\u00e4henemisen keskim\u00e4\u00e4rin. Rieszin energian avulla m\u00e4\u00e4ritell\u00e4\u00e4n my\u00f6s ns.\r\nkapasitiivinen dimensio jokaiselle euklidisen avaruuden Borel-joukolle. Ty\u00f6ss\u00e4 k\u00e4yd\u00e4\u00e4n l\u00e4pi my\u00f6s klassinen Frostmanin lemma euklidisen avaruuden F_\u03c3-joukoille, jonka perusteella t\u00e4llaisten joukkojen kapasitiiviset dimensiot yhtyv\u00e4t niiden Hausdorff-dimensioihin.\r\n\r\n\r\nToinen n\u00e4k\u00f6kulma ongelmaan otetaan tarkastelemalla yksikk\u00f6v\u00e4lin irrationaalilukujen Gaussin kuvauksen dynaamista systeemi\u00e4 ja siin\u00e4 olevia Gibbsin mittoja. Sopivalla reunaehdolla t\u00e4llaiset mitat v\u00e4henev\u00e4t aina polynomiaalisesti. Tarkastelu edellytt\u00e4\u00e4 kuitenkin symbolista dynamiikkaa, joka on my\u00f6s ty\u00f6ss\u00e4 yksi k\u00e4sitelty aihe.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Joonas Niinikoski (jokrniin) on 2016-09-27 16:58:19.052581. 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 2016-09-27T16:58:19Z\r\nNo. of bitstreams: 2\r\nURN:NBN:fi:jyu-201609274216.pdf: 1300187 bytes, checksum: c1b2e6c9307b33ab31f949757cf53655 (MD5)\r\nlicense.html: 4839 bytes, checksum: b057ab0eafb0825d90d6d63619200851 (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2016-09-27T16:58:19Z (GMT). No. of bitstreams: 2\r\nURN:NBN:fi:jyu-201609274216.pdf: 1300187 bytes, checksum: c1b2e6c9307b33ab31f949757cf53655 (MD5)\r\nlicense.html: 4839 bytes, checksum: b057ab0eafb0825d90d6d63619200851 (MD5)\r\n Previous issue date: 2016", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto (101 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": "\u00e4\u00e4rellinen Borel-mitta", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Fourier-muunnos", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Rajchman-mitta", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "polynomiaalinen v\u00e4heneminen", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Rieszin energia", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "kapasitiivinen dimensio", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Frostmanin lemma", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "symbolinen dynamiikka", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Gaussin kuvaus", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Gibbsin mitta", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Ruellen siirto-operaattori", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "\u00c4\u00e4rellisten Borel-mittojen Fourier-muunnoksista euklidisissa avaruuksissa", "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-201609274216", "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": 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"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.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"}]
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