dc.contributor.author |
El-Wali, Sara Mohamad. |
dc.date.accessioned |
2013-10-02T09:23:22Z |
dc.date.available |
2013-10-02T09:23:22Z |
dc.date.issued |
2013 |
dc.identifier.uri |
http://hdl.handle.net/10938/9632 |
dc.description |
Thesis (M.S.)--American University of Beirut, Department of Mathematics, 2013. |
dc.description |
Advisor : Dr. Bassam Shayya, Professor, Department of Mathematics--Committee Members : Dr. Michel Egeileh, Assisatnt Professor, Department of Mathematics ; Dr. Tamer Tlas, Assistant Professor, Department of Mathematics. |
dc.description |
Includes bibliographical references (leaf 60) |
dc.description.abstract |
One of the two important developments concerning the restriction theory in Fourier analysis during the last ten years was the development of the multi-linear restriction theory by Bennett, Carbery, and Tao in [2]. The second was the method introduced by Bourgain and Guth in [3] to convert multi-linear estimates to linear ones. In a recent paper [1], Bourgain used the method of [3] to obtain new results on exponential sums with frequencies E = DS for some hypersurface S with positive second fundamental form. Our thesis starts by explaining the Bourgain-Guth method in the plane and using it to give an alternative proof of the restriction theorem there. We then present the paper [1]. |
dc.format.extent |
vii, 60 leaves ; 30 cm. |
dc.language.iso |
eng |
dc.relation.ispartof |
Theses, Dissertations, and Projects |
dc.subject.classification |
T:005850 AUBNO |
dc.subject.lcsh |
Fourier analysis. |
dc.subject.lcsh |
Exponential sums. |
dc.subject.lcsh |
Dimensions. |
dc.title |
Recent estimates on exponential sums in higher dimensions |
dc.type |
Thesis |
dc.contributor.department |
American University of Beirut. Faculty of Arts and Sciences. Department of Mathematics. |