Sharp Barron Regularity Results for Coulombic Many-Electron Wave Functions
We establish sharp Barron regularity for Coulombic many-electron wave functions after extraction of the universal cut-off Jastrow factors. Following the factorization of Fournais et al.~\cite[Definition~1.4]{FournaisEtAl2005}, for a Coulombic eigenfunction $ψ$ we define the successive quotients by \[ φ=e^{-F_{2,\mathrm{cut}}}ψ\quad\text{and}\quad φ_3=e^{-F_{3,\mathrm{cut}}}φ=e^{-(F_{2,\mathrm{cut}}+F_{3,\mathrm{cut}})}ψ. \] Then \[ φ,φ_3\in\mathcal{B}^s(\mathbb{R}^{3N}) \qquad\text{for every }s<2. \] This range is optimal among universal factorizations. No factor depending only on the particle number and the nuclear data, but not on the eigenfunction or its eigenvalue, can make every corr...
| Authors | Pingbing Ming, Hao Yu |
|---|---|
| Primary category | math.AP |
| Published | 23 August 2026 |
| Last updated at source | 23 August 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.