컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0202 |
|---|---|
| 분류(Section) | Special Session |
| 분과(Session) | (SS-09) Harmonic Analysis and Related Topics (SS-09) |
| 발표시간(Time) | 19th-B-14:00 -- 14:30 |
| 영문제목 (Title(Eng.)) |
Oscillatory integral and sublevel-set estimates over global domains |
| 저자(Author(s)) |
Joonil Kim1 Yonsei University1 |
| 초록본문(Abstract) | Since Varchenko's seminal paper, the asymptotics of oscillatory integrals and related problems have been elucidated through the Newton polyhedra associated with the phase $P$. The supports of those integrals are concentrated on sufficiently small neighborhoods. This talk aims to investigate the estimates of sub-level-sets and oscillatory integrals whose supports are global domains $D$. A basic model of $D$ is $ \mathbb{R}^d$. For this purpose, we define the Newton polyhedra associated with $(P,D)$ and establish analogs of Varchenko's theorem in global domains $D$, under non-degeneracy conditions of $P$. Finally, we focus on its applications to Strichartz estimates and lattice counting problems associated with polynomials $P$. |
| 분류기호 (MSC number(s)) |
42B20, 42B25 |
| 키워드(Keyword(s)) | Sublevel set estimates, Newton polyhedra, faces and dual faces |
| 강연 형태 (Language of Session (Talk)) |
Korean |