发表机构
Soochow University; Central South University（苏州大学; 中南大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究Bargmann–Fock空间在临界密度下精确零点集的刻画问题，证明经典密度理论失效，并提出基于重整化对数势和相对熵的变分判据，为临界构型提供尖锐条件。
AI 中文摘要
在临界密度下，Bargmann–Fock空间的经典密度理论不再能确定精确的零点集。我们证明这种失效是实质性的：完整的径向计数函数连同任意给定的有限角矩集合无法确定精确可实现性，并且消失空间维数与零点插入容量之间的有限维关系在无限维中失效。对于任意局部有限多重集，我们建立了精确零点集的一个变分刻画，该刻画基于重整化对数势和相对熵。这一刻画为几类临界构型提供了尖锐的判据。
英文摘要
At the critical density, the classical density theory of the Bargmann--Fock space no longer determines exact zero sets. We show that this failure is substantial: the complete radial counting function together with any prescribed finite collection of angular moments does not determine exact realizability, and the finite-dimensional relation between the dimension of the vanishing space and the zero-insertion capacity breaks down in infinite dimension. For arbitrary locally finite multisets, we establish a variational characterization of exact zero sets in terms of a renormalized logarithmic potential and relative entropy. This characterization yields sharp criteria for several classes of critical configurations.
