dc.contributor.advisor | Iosevich, Alex, 1967- | eng |
dc.contributor.author | Koh, Doowon, 1972- | eng |
dc.date.issued | 2008 | eng |
dc.date.submitted | 2008 Fall | eng |
dc.description | Title from PDF of title page (University of Missouri--Columbia, viewed on November 9, 2010). | eng |
dc.description | The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. | eng |
dc.description | Dissertation advisor: Dr. Alex Iosevich. | eng |
dc.description | Vita. | eng |
dc.description | |Ph. D. University of Missouri--Columbia 2008. | eng |
dc.description.abstract | We study the L[superscript p] - L[superscript r] boundedness of the extension operator associated with algebraic varieties such as nondegenerate quadratic surfaces, paraboloids, and cones in vector spaces over finite fields. We obtain the best possible result for the extension theorems related to nondegenerate quadratic curves in two dimensional vector spaces over finite fields. In higher even dimensions, we improve upon the Tomas-Stein exponents which were obtained by Mockenhaupt and Tao ([21]) by studying extension theorems for paraboloids in the finite field setting. We also study extension theorems for cones in vector spaces over finite fields. We give an alternative proof of the best possible result for the extension theorems for cones in three dimensions, which originally is due to Mockenhaupt and Tao ([21]). Moreover, our method enables us to obtain the sharp L[2] - L[superscript r] estimate of the extension operator for cones in higher dimensions. In addition, we study the relation between extension theorems for spheres and the Erdos-Falconer distance problems in the finite field setting. Using the sharp extension theorem for circles, we improve upon the best known result, due to A. Iosevich and M. Rudnev ([17]), for the Erdos-Falconer distance problems in two dimensional vector spaces over finite fields. Discrete Fourier analytic machinery, arithmetic considerations, and classical exponential sums play an important role in the proofs. | eng |
dc.description.bibref | Includes bibliographical references (p. 86-89). | eng |
dc.format.extent | 90 pages | eng |
dc.identifier.oclc | 681912406 | eng |
dc.identifier.uri | https://hdl.handle.net/10355/9097 | |
dc.identifier.uri | https://doi.org/10.32469/10355/9097 | eng |
dc.language | English | eng |
dc.publisher | University of Missouri--Columbia | eng |
dc.relation.ispartofcommunity | University of Missouri--Columbia. Graduate School. Theses and Dissertations | eng |
dc.rights | OpenAccess. | eng |
dc.rights.license | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. | |
dc.subject.lcsh | Fourier analysis | eng |
dc.subject.lcsh | Vector spaces | eng |
dc.subject.lcsh | Quadratic fields | eng |
dc.subject.lcsh | Paraboloid | eng |
dc.subject.lcsh | Finite fields (Algebra) | eng |
dc.subject.lcsh | Field extensions (Mathematics) | eng |
dc.title | Extension theorems in vector spaces over finite fields | eng |
dc.type | Thesis | eng |
thesis.degree.discipline | Mathematics (MU) | eng |
thesis.degree.grantor | University of Missouri--Columbia | eng |
thesis.degree.level | Doctoral | eng |
thesis.degree.name | Ph. D. | eng |