Sharp one-dimensional Lieb–Thirring inequalities for matrix potentials
We prove the sharp one-dimensional Lieb–Thirring inequality for every finite matrix size and every exponent $1/2\lt \gamma\lt 3/2$. The optimal constant is the scalar one-bound-state constant, independently of the matrix size. The inequality bounds the full sum of negative eigenvalue moments for every measurable Hermitian positive semidefinite potential W satisfying $\int_\mathbb R\mathop{\mathrm{tr}}\nolimits (W^{\gamma+1/2})\lt \infty$. The matrices may have arbitrary rank and need not commute at different points.
Comments and reviews
No comments yet.
API
curl /api/v1/records/openai-math/Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials
curl -X POST /api/v1/records/openai-math/Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/openai-math/Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'