PreprintCC BY 4.0arXiv
Separation for Schrödinger operators. A counterexample to Simon's conjecture
Abstract
We construct, for every d≥ 5, a nonnegative radial potential V∈ L∞loc(ℝd∖{0})∩ L1(ℝd) for which V(−Δdotplus V)−1 is not bounded on L2(ℝd).
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BibTeX
@misc{perelmuter2026separation,
title = {{Separation for Schrödinger operators. A counterexample to Simon's conjecture}},
author = {M. A. Perelmuter},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00415},
eprint = {2609.00415},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00415},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Separation for Schrödinger operators. A counterexample to Simon's conjecture
AU - M. A. Perelmuter
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00415
UR - https://arxiv.org/abs/2609.00415
AB - We construct, for every d≥ 5, a nonnegative radial potential V∈ L^∞_loc(ℝ^d∖{0})∩ L^1(ℝ^d) for which V(−Δdotplus V)^−1 is not bounded on L^2(ℝ^d).
ER -