Mathematical Sciences: Heat Flow Estimates and Berezin-Toeplitz Algebras

Coburn将继续在几个方向上研究热流估计和Berezin-Toeplitz代数。将继续努力发展“反向热估计”，这是由伯杰早期工作中通常的热方程得到的，以更一般的抛物方程。另一个重点将是跟进最近与J. Xia关于“Toeplitz代数和Rieffel变形”的工作，以检查有界域上的Toeplitz代数是否通常是连续函数对应代数的“严格变形量化”。Coburn和Berger还将继续Coburn关于“Berezin-Toeplitz量化的变形估计”的工作，以获得（玻色子）正则交换关系代数的同构不变量。这些不变量是将指标定理适当地推广到带有“最终缓慢变化”符号的伪微分算子而产生的。＊＊＊

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. ***