Extension theorems for the Fourier transform associated with non-degenerate quadratic surfaces in vector spaces over finite fields

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dc.creatorIosevich, Alex
dc.creatorKoh, Doowon
dc.date2008-04-28
dc.date.accessioned2026-07-07T09:35:48Z
dc.date.available2026-07-07T09:35:48Z
dc.descriptionWe study the restriction of the Fourier transform to quadratic surfaces in vector spaces over finite fields. In two dimensions, we obtain the sharp result by considering the sums of arbitrary two elements in the subset of quadratic surfaces on two dimensional vector spaces over finite fields. For higher dimensions, we estimate the decay of the Fourier transform of the characteristic functions on quadratic surfaces so that we obtain the Tomas-Stein exponent. Using incidence theorems, we also study the extension theorems in the restricted settings to sizes of sets in quadratic surfaces. Estimates for Gauss and Kloosterman sums and their variants play an important role.
dc.description18 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/0804.4505
dc.identifierhttp://arxiv.org/abs/0804.4505
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159950
dc.subjectClassical Analysis and ODEs
dc.subject43A15; 43A32
dc.titleExtension theorems for the Fourier transform associated with non-degenerate quadratic surfaces in vector spaces over finite fields
dc.typetext

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