dc.contributor.advisor | Lyubarskii, Yurii | nb_NO |
dc.contributor.author | Aksnes, Vegard | nb_NO |
dc.date.accessioned | 2014-12-19T13:57:49Z | |
dc.date.available | 2014-12-19T13:57:49Z | |
dc.date.created | 2010-09-04 | nb_NO |
dc.date.issued | 2007 | nb_NO |
dc.identifier | 348439 | nb_NO |
dc.identifier | ntnudaim:1498 | nb_NO |
dc.identifier.uri | http://hdl.handle.net/11250/258376 | |
dc.description.abstract | We 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.language | eng | nb_NO |
dc.publisher | Institutt for matematiske fag | nb_NO |
dc.subject | ntnudaim | no_NO |
dc.subject | MMA matematikk | no_NO |
dc.subject | Analyse | no_NO |
dc.title | On Fourier Series in Convex Domains | nb_NO |
dc.type | Master thesis | nb_NO |
dc.source.pagenumber | 116 | nb_NO |
dc.contributor.department | Norges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikk, Institutt for matematiske fag | nb_NO |