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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 沈俊嚴 | zh_TW |
| dc.contributor.advisor | Chun-Yen Shen | en |
| dc.contributor.author | 何世宇 | zh_TW |
| dc.contributor.author | Shih-Yu Ho | en |
| dc.date.accessioned | 2023-08-09T16:48:51Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-08-09 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-07-26 | - |
| dc.identifier.citation | Jean Bourgain. Hausdorff dimension and distance sets. Israel Journal of Math ematics, 87:193-201, 1994
Xiumin Du, Alex Iosevich, Yumeng Ou, Hong Wang, and Ruixiang Zhang. An improved result for falconer’s distance set problem in even dimensions. Mathematische Annalen, 380:1215–1231, 2021 M Burak Erdog̃an. A bilinear fourier extension theorem and applications to the distance set problem. International Mathematics Research Notices, 2005(23):1411–1425, 2005 Kenneth J Falconer. On the hausdorff dimensions of distance sets. Mathematika, 32(2):206–212, 1985 CHARLES LOUIS FEFFERMAN. Inequalities for strongly singular convolu tion operators. Princeton University, 1969 Larry Guth, Alex Iosevich, Yumeng Ou, and Hong Wang. On falconer’s distance set problem in the plane. Inventiones mathematicae, 219(3):779–830, 2020 Pertti Mattila. Spherical averages of fourier transforms of measures with finite energy; dimensions of intersections and distance sets. Mathematika, 34(2):207–228, 1987 Pertti Mattila. Geometry of sets and measures in Euclidean spaces: fractals and rectifiability. Number 44. Cambridge university press, 1999 Pertti Mattila. Fourier Analysis and Hausdorff Dimension. Number 150. Cam bridge University Press, 2015 Christopher D Sogge. Fourier integrals in classical analysis, volume 210. Cam bridge University Press, 2017 Elias M Stein. Interpolation of linear operators. Transactions of the American Mathematical Society, 83(2):482–492, 1956 Elias M Stein. Oscillatory integrals in fourier analysis. Beijing lectures in harmonic analysis, 112:307–355, 1986 Terence Tao. A sharp bilinear restriction estimate for paraboloids. Geometric & Functional Analysis GAFA, 13:1359–1384, 2003 P Tomas et al. A restriction theorem for the fourier transform. Bull. Amer.Math. Soc, 81, 1975 Thomas Wolff. Decay of circular means of fourier transforms of measures. International Mathematics Research Notices, 1999(10):547–567, 1999 | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/88382 | - |
| dc.description.abstract | 本論文的目的是研究歐幾里得空間中的傅立葉限制問題及其在法爾科納距離集猜想中的應用。限制問題是調和分析領域中最知名的研究問題之一，且與其他研究領域（如偏微分方程和幾何測度論）有著重要的聯繫。在本論文中，我們主要詳細介紹已知的Tomas-Stein成果、雙線性限制估計以及Bourgain對法爾科納距離猜想的結果。 | zh_TW |
| dc.description.abstract | The purpose of this dissertation is to study the Fourier restriction problems in Euclidean spaces and their applications to Falconer's distance set conjecture. Restriction problems are one of the most known research problems in the area of Harmonic analysis and have been found to have important connections to other research fields such as partial differential equations and geometric measure theory. In this dissertation, we mainly introduce in details the known Tomas-Stein results, bilinear restriction estimates and Bourgain's work on Falconer distance conjecture. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-08-09T16:48:51Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-08-09T16:48:51Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 致謝 i
摘要 ii Abstract iii List of Figures v 1 Introduction 1 2 Introduction of restriction problems and the results of Tomas and Stein 4 2.1 Some Known Results of Restriction Problem 4 2.2 Proof of Tomas-Stein Restriction Theorem 9 2.3 Conclusion of Restriction Conjecture 19 3 Connections between restriction problems and geometric measure theory 21 3.1 The case for n = 2 21 3.2 The case for n ≥ 3 35 References 52 | - |
| dc.language.iso | en | - |
| dc.subject | 幾何測度論 | zh_TW |
| dc.subject | 傅立葉限制問題 | zh_TW |
| dc.subject | Tomas-Stein定理 | zh_TW |
| dc.subject | 福爾科納猜想 | zh_TW |
| dc.subject | 調和分析 | zh_TW |
| dc.subject | geometric measure theory | en |
| dc.subject | Fourier restriction problems | en |
| dc.subject | Falconer's conjecture | en |
| dc.subject | Tomas-Stein theorem | en |
| dc.subject | harmonic analysis | en |
| dc.title | 歐氏空間之傅立葉變換限制問題的探討 | zh_TW |
| dc.title | A Survey of The Restriction Problems in Euclidean Spaces | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 陳逸昆;李冀 | zh_TW |
| dc.contributor.oralexamcommittee | I-Kun Chen;Ji Li | en |
| dc.subject.keyword | 幾何測度論,Tomas-Stein定理,傅立葉限制問題,福爾科納猜想,調和分析, | zh_TW |
| dc.subject.keyword | Tomas-Stein theorem,geometric measure theory,Fourier restriction problems,Falconer's conjecture,harmonic analysis, | en |
| dc.relation.page | 53 | - |
| dc.identifier.doi | 10.6342/NTU202301952 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2023-07-27 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 數學系 | - |
| 顯示於系所單位： | 數學系 | |
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