S-Space College of Natural Sciences (자연과학대학) Dept. of Mathematical Sciences (수리과학부) Theses (Master's Degree_수리과학부)
Fourier restriction estimates for space curves
공간 곡선에 대한 푸리에 제한 계측
- 자연과학대학 수리과학부
- Issue Date
- 서울대학교 대학원
- Fourier restriction estimates for space curves; non-degenerate curve; Lorentz space; Hausdorff-Young inequality
- 학위논문 (석사)-- 서울대학교 대학원 : 자연과학대학 수리과학부, 2018. 2. 이상혁.
- For the Fourier transformation of a Schwartz function f, one can ask for which p, q and subsets S we can meaningfully restrict the Fourier transform. That is, what geometrical property of a set S makes it possible to have the estimate.
In this paper, we will cover cases when a set S is a curve with certain non-degeneracy property. The purpose of this paper is to survey historical progress to deal with local restriction estimates for non-degenerate curves. Doing this, we review methods related to the restriction theorem and limitations come from those methods.