Spectral Asymptotics for Non-self-adjoint Semiclassical Operators

非自伴半经典算子的谱渐近

• 批准号: 0304970
• 负责人: James Ralston
• 金额: $ 9.05万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0304970&HistoricalAwards=false
• 关键词: Spectral; Asymptotics; Non; self; adjoint

PI: James V. Ralston (for Hatrik), UCLADMS-0304970ABSTRACT This proposal presents problems in spectral theory of non-self-adjoint differential operators in the semi-classical regime. The proposer seeks precise estimates on the asymptotic behavior of the eigenvalues of small perturbations of self-adjoint operators on compact domains in several settings. In closely related projects he plans to apply recently developed techniques to the problem of finding asymptotics (counting functions) for the scattering poles associated withconvex obstacles and the barrier top resonances for Schroedinger operators.This work studies the propagation of waves in settings where some form of dissipation or the possibility of propagation to infinity gives rise to waves which decay to zero as time increases. The rates of decay and frequency of these decaying modes are encoded in sequences of complex eigenvalues or resonances associated with these problems. Studying the behavior of these sequences can lead to better understanding of the relation between rates of decay and theunderlying structure of the system. Such information has potential application in determining the interior structure of objects from their resonant frequencies in nondestructive testing.

PI：James V. Ralston（对于Hatrik），Ucladms-0304970Abstractrats该提案在半经典制度中提出了非自由选择差异操作员的光谱理论。提议者在几种情况下，在紧凑型域上自偶会操作员对紧凑型域的小扰动的渐近行为寻求精确的估计。在紧密相关的项目中，他计划将最近开发的技术应用于与conconvex障碍相关的散射两极的问题（计数功能）的问题，以及Schroedinger操作员的障碍最高共振。这项工作研究在某些形式的散发形式的散发浪潮中，在某些形式的散发或Infiniencation to Infiniencation to Infiniencation tige aidge serie and cisse aise dise dise deceay dise deceay serative of decay sew of。这些衰减模式的衰减和频率的速率以与这些问题相关的复杂特征值或共振的序列进行编码。研究这些序列的行为可以更好地理解系统的衰减速率与底层结构之间的关系。此类信息具有潜在的应用，可以在非损害测试中从其谐振频率中确定对象的内部结构。