Family 262Mathematical physicsLeanNot yet digested
Sharp finite-matrix Lieb–Thirring inequalities and all equality cases
Proves the sharp one-dimensional Lieb–Thirring inequality for and arbitrary finite-matrix potentials W ≥ 0 with : the optimal constant is the scalar one-bound-state value, independent of matrix size. All equality cases are direct sums, in one constant unitary basis, of scalar sech solitons with independent scales and centers, and zero channels.
Manuscripts in this family · 3
Equality cases in the sharp one-dimensional matrix Lieb–Thirring inequality
Oct 5, 2026·sharp-one-dimensional-lieb-thirring-inequalities-matrix-potentials.pdf
We classify all equality cases in the sharp one-dimensional Lieb–Thirring inequality for every finite matrix size and . For measurable Hermitian positive semidefinite potentials W with , equality holds precisely for direct sums, in one constant unitary basis, of scalar one-bound-state solitons and zero channels. The nonzero solitons may have independent scales and centers.
Sharp one-dimensional Lieb–Thirring inequalities for matrix potentials
Oct 5, 2026·sharp-matrix-lieb-thirring.pdf
We prove the sharp one-dimensional Lieb–Thirring inequality for every finite matrix size and every exponent . 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 . The matrices may have arbitrary rank and need not commute at different points.
Sharp one-dimensional Lieb–Thirring constants
Sep 23, 2026·paper.pdfLean
We resolve affirmatively the remaining cases of the scalar one-dimensional Lieb–Thirring conjecture: for every , the optimal constant is the one-bound-state constant. The estimate holds for every nonnegative potential in , with all negative eigenvalues included.