Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Hou, Shengzhao, Ma, Pan
Institutions: Soochow University, Central South University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214942637