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dc.contributor.advisorLyubarskii, Yuriinb_NO
dc.contributor.authorAksnes, Vegardnb_NO
dc.date.accessioned2014-12-19T13:57:49Z
dc.date.available2014-12-19T13:57:49Z
dc.date.created2010-09-04nb_NO
dc.date.issued2007nb_NO
dc.identifier348439nb_NO
dc.identifierntnudaim:1498nb_NO
dc.identifier.urihttp://hdl.handle.net/11250/258376
dc.description.abstractWe consider systems of complex exponential functions in spaces of square integrable functions. Some classical one-dimensional theory is reviewed, in particular, we emphasize the duality between the Riesz bases of complex exponential functions in $L^2$-spaces and complete interpolating sequences in $PW^2$-spaces of entire functions of exponential type. Basis properties for $L^2$-spaces over planar convex domains are then studied in detail. The convex domain in question is shown to be crucial for what basis properties the corresponding $L^2$-space possesses. We explain some results related to Fuglede's conjecture about existence of orthonormal bases and then a result by Lyubarskii and Rashkovskii regarding Riesz bases for $L^2$-spaces over convex polygons, symmetric with respect to the origin. Finally, we make a modest attempt to apply the techniques by Lyubarskii and Rashkovskii combined with approximation of plurisubharmonic functions using logarithms of moduli of entire functions, to construct a complete system of exponential functions in the space of square integrable functions over a disk. This work is not completed yet.nb_NO
dc.languageengnb_NO
dc.publisherInstitutt for matematiske fagnb_NO
dc.subjectntnudaimno_NO
dc.subjectMMA matematikkno_NO
dc.subjectAnalyseno_NO
dc.titleOn Fourier Series in Convex Domainsnb_NO
dc.typeMaster thesisnb_NO
dc.source.pagenumber116nb_NO
dc.contributor.departmentNorges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikk, Institutt for matematiske fagnb_NO


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