Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.662516
Title: Aspects of harmonic analysis over finite fields
Author: Stones, Brendan
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2005
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Abstract:
In this thesis we study three topics in Harmonic Analysis in the finite field setting. The methods used are purely combinatorial in nature. We prove a sharp result for the maximal operator associated to dilations of quadric surfaces. We use Christ’s method ([Christ, Convolution, Curvature and Combinatorics. A case study, International Math. Research Notices 19 (1998)]), for Lp→ Lq estimates for convolution with the twisted n-bic curve in the European setting, to give Lp → Lq estimates for convolution with k-dimensional surfaces in the finite field setting. We give solution to the k-plane Radon transform problem and embark on a study of a generalisation of this problem.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.662516  DOI: Not available
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