Mathematical Sciences: Heat Flow Estimates and Berezin-Toeplitz Algebras

数学科学：热流估计和 Berezin-Toeplitz 代数

• 批准号: 9500716
• 负责人: Lewis Coburn
• 金额: $ 7.5万
• 依托单位: SUNY at Buffalo
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500716&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Heat; Flow; Estimates

9500716 Coburn Coburn will continue studies of heat flow estimates and Berezin-Toeplitz algebras in several directions. Efforts will be continued to develop "backward heat estimates", obtained for the usual heat equation in earlier work with C. A. Berger, to more general parabolic equations. Another focus will be to follow-up recent work with J. Xia on "Toeplitz algebras and Rieffel deformations" to check whether Toeplitz algebras on bounded domains are generally "strict deformation quantizations" of the corresponding algebras of continuous functions. Coburn and Berger will also follow-up Coburn's work on "Deformation estimates for the Berezin-Toeplitz quantization" to obtain isomorphism invariants for the algebras of (boson) canonical commutation relations. These invariants arise from an appropriate extension of the index theorem to pseudo-differential operators with "eventually slowly varying" symbols. ***

9500716 Coburn Coburn将在几个方向上继续研究热流估计和Berezin-Toeplitz代数。我们将继续努力将“倒向热估计”发展为更一般的抛物型方程。“倒向热估计”是在与C.A.Berger的早期工作中对通常的热方程得出的。另一个焦点将是与J.Xia最近在“Toeplitz代数和Rieffel变形”方面的工作的后续工作，以检验有界域上的Toeplitz代数是否通常是连续函数的相应代数的“严格形变量化”。Coburn和Berger还将继续Coburn关于Berezin-Toeplitz量子化的变形估计的工作，以获得(玻色子)正则对易关系的代数的同构不变量。这些不变量是将指数定理适当地推广到符号“最终缓慢变化”的伪微分算子而产生的。***