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Fourier restriction estimates for space curves
| Content Provider | Semantic Scholar |
|---|---|
| Author | Park, Jungwon |
| Copyright Year | 2008 |
| Abstract | Fourier restriction estimates for space curves Jungwon Park Department of Mathematical Sciences Seoul National University For the Fourier transformation f̂(y) = ∫ e−iy·xf(x)dx of a Schwartz function f , one can ask for which p, q and subsets S ⊂ R we can meaningfully restrict the Fourier transform. That is, what geometrical property of a set S makes it possible to have the estimate ∥∥∥f̂∥∥∥ Lp ∗ (S,dμ) ≤ Cp ‖f‖p . In this paper, we will cover cases when a set S is a curve with certain nondegeneracy 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. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://s-space.snu.ac.kr/bitstream/10371/142450/1/000000149278.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
