English

Counterexample to the Laptev--Safronov conjecture

Spectral Theory 2022-11-30 v1 Mathematical Physics Analysis of PDEs math.MP

Abstract

We prove that the Laptev--Safronov conjecture (Comm. Math. Phys., 2009) is false in the range that is not covered by Frank's positive result (Bull. Lond. Math. Soc., 2011). The simple counterexample is adaptable to a large class of Schr\"odinger type operators, for which we also prove new sharp upper bounds.

Keywords

Cite

@article{arxiv.2109.06135,
  title  = {Counterexample to the Laptev--Safronov conjecture},
  author = {Sabine Bögli and Jean-Claude Cuenin},
  journal= {arXiv preprint arXiv:2109.06135},
  year   = {2022}
}

Comments

20 pages

R2 v1 2026-06-24T05:55:36.986Z