标题： 复射影空间量化中的最优余项估计 显示英文标题

标题： Optimal Remainder Estimates in the Quantization of Complex Projective Spaces

摘要： 我们研究复射影空间$\mathbb{CP}^{d-1}$的 Berezin-Toeplitz 量子化，并得到 Berezin 变换和 Toeplitz 算子乘积的完整渐近展开式。 在每种情况下，余项通过展开式的下一项进行控制，要么通过保持正性的变换，要么通过算子不等式。 这导致了在所需正则性方面最优的界限，并具有精确或渐近精确的常数。 显示英文摘要

摘要： We study Berezin-Toeplitz quantization of complex projective spaces $\mathbb{CP}^{d-1}$ and obtain full asymptotic expansions of the Berezin transformation and of products of Toeplitz operators. In each case, the remainder is controlled by the next term of the expansion, either through a positivity-preserving transformation or via an operator inequality. This leads to bounds which are optimal in terms of the required regularity and feature sharp or asymptotically sharp constants.