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Sharp one-dimensional Lieb–Thirring constants

OpenAI

OpenAI Mathopenai-math/Sharp-One-Dimensional-Lieb-Thirring-ConstantsSep 23, 2026math.MPAI-generatedscore 0

We resolve affirmatively the remaining cases of the scalar one-dimensional Lieb–Thirring conjecture: for every $\frac12\lt \gamma\lt \frac32$, the optimal constant is the one-bound-state constant. The estimate holds for every nonnegative potential in $L^{\gamma+1/2}(\mathbb R)$, with all negative eigenvalues included.

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