Hardy inequalities for large fermionic systems
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Given 0 < s < d/2 with s ≤ 1, we are interested in the large N-behavior of the optimal constant κN in the Hardy inequality ΣNn=1(-Δn)s ≥ κN Σn<m |Xn - Xm|-2s, when restricted to antisymmetric functions. We show that N1-2s/d κN has a positive, finite limit given by a certain variational problem, thereby generalizing a result of Lieb and Yau related to the Chandrasekhar theory of gravitational collapse.
Originalsprog | Engelsk |
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Tidsskrift | Journal of Spectral Theory |
Vol/bind | 14 |
Udgave nummer | 2 |
Sider (fra-til) | 805-835 |
ISSN | 1664-039X |
DOI | |
Status | Udgivet - 2024 |
Bibliografisk note
Funding Information:
Funding. RLF was partially supported by the US National Science Foundation Grant number DMS-1954995 and the DFG grants EXC-2111-390814868 and TRR 352-Project-ID 470903074. The support of the villum Centre of Excellence for the Mathematics of Quantum Theory (QMATH) Grant number 10059 to JPS is acknowledged.
Publisher Copyright:
©2024 European Mathematical Society.
ID: 396649709