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摘要翻译：
近年来，极化复射影流形的Szeg{o}核的等变分量的Tian-Zelditch渐近展开及其在标度极限方面的推广，在代数、辛和微分几何中发挥了重要作用。一个自然的问题是，是否存在这样的推广，即全纯截面空间上的投影仪可以被更一般的（非完全的）线性级数上的投影仪所代替。从几何量子化的观点来看，这种分析是很自然的一种情况，它是由对一个不变的自伴Toeplitz算子施加谱界而确定的线性级数给出的。在本文中，我们重点讨论了与缓慢收缩谱带相关的光谱投影的渐近性。
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英文标题：
《Equivariant asymptotics for Toeplitz operators》
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作者：
Roberto Paoletti
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Spectral Theory 光谱理论
分类描述：Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices
薛定谔算子，流形上的算子，一般微分算子，数值研究，积分算子，离散模型，共振，非自伴算子，随机算子/矩阵
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Complex Variables 复变数
分类描述：Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数，自守群作用与形式，伪凸性，复几何，解析空间，解析束
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一级分类：Mathematics 数学
二级分类：Symplectic Geometry 辛几何
分类描述：Hamiltonian systems, symplectic flows, classical integrable systems
哈密顿系统，辛流，经典可积系统
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英文摘要：
In recent years, the Tian-Zelditch asymptotic expansion for the equivariant components of the Szeg\"{o} kernel of a polarized complex projective manifold, and its subsequent generalizations in terms of scaling limits, have played an important role in algebraic, symplectic, and differential geometry. A natural question is whether there exist generalizations in which the projector onto the spaces of holomorphic sections can be replaced by the projector onto more general (non-complete) linear series. One case that lends itself to such analysis, and which is natural from the point of view of geometric quantization, is given by the linear series determined by imposing spectral bounds on an invariant self-adjoint Toeplitz operator. In this paper we focus on the asymptotics of the spectral projectors associated to slowly shrinking spectral bands.
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PDF链接：
https://arxiv.org/pdf/0810.2305
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