AI 中文总结
本文利用Parseval框架的排除原理，为径向成本下的族成本提供下界，并导出半经典极限与Toeplitz能量渐近，应用于多种函数空间与系综。
AI 中文摘要
设一个归一化的连续Parseval框架描述再生核希尔伯特空间的相空间。一个正交族的框架系数的总质量等于状态数，而逐点质量至多为1。这一基本的排除原理给出了族的总成本在低成本区域体积方面的显式下界。对于径向成本，它导出了集体均值-离差、伞形和输运不等式。同样的论证适用于归一化的Bessel族，其中Bessel界度量允许的重叠。我们还考虑了框架测度变化的半经典族。归一化测度的弱收敛，连同归一化核的平均局部化，产生了连续符号Szegő极限和最低Toeplitz能量的尖锐渐近。这些结果适用于Bargmann--Fock和加权Bergman空间、Gabor和Paley--Wiener空间，以及正交多项式和行列式系综，包括GUE。
英文摘要
Let a normalized continuous Parseval frame describe the phase space of a reproducing kernel Hilbert space. The frame coefficients of an orthonormal family have total mass equal to the number of states and pointwise mass at most one. This elementary exclusion principle gives explicit lower bounds for the total cost of a family in terms of the volume of low-cost regions. For radial costs, it yields collective mean-dispersion, umbrella, and transport inequalities. The same argument applies to normalized Bessel families, with the Bessel bound measuring the permitted overlap. We also consider semiclassical families for which the frame measures vary. Weak convergence of the normalized measures, together with averaged localization of the normalized kernels, yields continuous-symbol Szegő limits and sharp asymptotics for the lowest Toeplitz energies. The results apply to Bargmann--Fock and weighted Bergman spaces, Gabor and Paley--Wiener spaces, and orthogonal-polynomial and determinantal ensembles, including the GUE.
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