Three problems in Harmonic Analysis
谐波分析中的三个问题
基本信息
- 批准号:1201474
- 负责人:
- 金额:$ 9.62万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2012
- 资助国家:美国
- 起止时间:2012-06-01 至 2017-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
In this mathematics research project, the focus is on three different problems in harmonic analysis. The first one is on a divergence-curl type estimate on a large class of non-abelian homogeneous Lie groups that includes the Heisenberg group as the simplest, nontrivial model. The second one is about the construction of a certain class of pseudodifferential operators that are adapted to two different flags; these operators will then be used to study the solution operators of certain partial differential equations that arise naturally in the study of several complex variables. The third problem is about a class of nonlinear wave equations whose elliptic parts exhibit conformal invariance, and we bring in elements from conformal geometry in studying these wave equations. These problems present interesting challenges from the analytical point of view.Broadly speaking, harmonic analysis studies functions or signals by decomposing them into different frequencies. Its applications are abundant, ranging from signal processing and tomography to problems arising from physics such as relativity and quantum mechanics. Yung and his collaborators will investigate some deep and fundamental questions in harmonic analysis, along with its connections to other areas of mathematics such as several complex variables and conformal geometry. In particular, in one of the proposed projects, a study of how certain nonlinear waves propagate through space will be carried out. The research will be in collaboration both with faculties that are experts in the field, as well as some young researchers who are just starting their research careers.
在这个数学研究项目中,重点是调和分析中的三个不同问题。第一个是一个大类的非阿贝尔齐次李群,其中包括海森堡组作为最简单的,非平凡的模型上的发散旋度型估计。第二个是关于构造一类适用于两个不同标志的伪微分算子;然后这些算子将用于研究某些偏微分方程的解算子,这些偏微分方程在研究多个复变量时自然出现。第三个问题是关于一类椭圆部分具有共形不变性的非线性波动方程,我们引入了共形几何中的元素来研究这类波动方程。从分析的角度来看,这些问题提出了有趣的挑战。广义地说,谐波分析通过将函数或信号分解为不同的频率来研究它们。它的应用是丰富的,从信号处理和断层扫描到相对论和量子力学等物理学问题。Yung和他的合作者将研究调和分析中的一些深刻和基本的问题,沿着它与数学的其他领域的联系,如几个复变量和共形几何。特别是,在其中一个拟议项目中,将对某些非线性波如何在空间中传播进行研究。这项研究将与该领域的专家以及一些刚刚开始研究生涯的年轻研究人员合作。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Sagun Chanillo其他文献
LPEstimates for fractional integrals and sobolev inequalities with applications to schrödinger operators
分数积分和索博列夫不等式的 LPE 估计及其在薛定谔算子中的应用
- DOI:
10.1080/03605308508820401 - 发表时间:
1985 - 期刊:
- 影响因子:0
- 作者:
Sagun Chanillo;R. Wheeden - 通讯作者:
R. Wheeden
Variations on a proof of a borderline Bourgain-Brezis Sobolev embedding theorem
- DOI:
10.1007/s11401-016-1069-y - 发表时间:
2017-01-05 - 期刊:
- 影响因子:0.500
- 作者:
Sagun Chanillo;Jean Van Schaftingen;Po-Lam Yung - 通讯作者:
Po-Lam Yung
Conformal Geometry and the Composite Membrane Problem
共形几何和复合膜问题
- DOI:
10.2478/agms-2012-0002 - 发表时间:
2012 - 期刊:
- 影响因子:1
- 作者:
Sagun Chanillo - 通讯作者:
Sagun Chanillo
WEIGHTED POINCARE AND SOBOLEV INEQUALITIES AND ESTIMATES FOR WEIGHTED PEANO MAXIMAL FUNCTIONS
加权Poincare和Sobolev不等式以及加权PEANO极大值函数的估计
- DOI:
10.2307/2374351 - 发表时间:
1985 - 期刊:
- 影响因子:1.7
- 作者:
Sagun Chanillo;R. Wheeden - 通讯作者:
R. Wheeden
Regularity of the minimizers in the composite membrane problem in R^2
R^2复合膜问题中极小值的正则性
- DOI:
10.1016/j.jfa.2008.04.015 - 发表时间:
2008 - 期刊:
- 影响因子:0
- 作者:
Sagun Chanillo;Carlos E.Kenig;TO Tung - 通讯作者:
TO Tung
Sagun Chanillo的其他文献
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{{ truncateString('Sagun Chanillo', 18)}}的其他基金
Mathematical Sciences: Harmonic Analysis and Partial Differential Equations
数学科学:调和分析和偏微分方程
- 批准号:
9623079 - 财政年份:1996
- 资助金额:
$ 9.62万 - 项目类别:
Standard Grant
Mathematical Sciences: Problems in Harmonic Analysis and PDE
数学科学:调和分析和偏微分方程问题
- 批准号:
9401782 - 财政年份:1994
- 资助金额:
$ 9.62万 - 项目类别:
Standard Grant
Mathematical Sciences: Harmonic Analysis and Partial Differential Equations
数学科学:调和分析和偏微分方程
- 批准号:
9202051 - 财政年份:1992
- 资助金额:
$ 9.62万 - 项目类别:
Standard Grant
Mathematical Sciences: Harmonic Analysis Related To Weight Functions
数学科学:与权函数相关的调和分析
- 批准号:
8803493 - 财政年份:1988
- 资助金额:
$ 9.62万 - 项目类别:
Continuing Grant
Mathematical Sciences: Problems in Harmonic Analysis Relatedto Weight Functions
数学科学:与权函数相关的调和分析问题
- 批准号:
8601119 - 财政年份:1986
- 资助金额:
$ 9.62万 - 项目类别:
Standard Grant
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