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arXiv · 2609.00415

Separation for Schr\"odinger operators. A counterexample to Simon's conjecture

M. A. Perelmuter
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Abstract

We construct, for every $d\ge 5$, a nonnegative radial potential $V\in L^\infty_{\mathrm{loc}}(\mathbb{R}^d\setminus\{0\})\cap L^1(\mathbb{R}^d)$ for which $V(-\Delta\dotplus V)^{-1}$ is not bounded on $L^2(\mathbb{R}^d)$.

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M. A. Perelmuter. 2026-08-31. Separation for Schr\"odinger operators. A counterexample to Simon's conjecture. https://arxiv.org/abs/2609.00415

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