Equality cases in the sharp one-dimensional matrix Lieb–Thirring inequality
We classify all equality cases in the sharp one-dimensional Lieb–Thirring inequality for every finite matrix size and $1/2\lt \gamma\lt 3/2$. For measurable Hermitian positive semidefinite potentials W with $\int_\mathbb R\mathop{\mathrm{tr}}\nolimits (W^{\gamma+1/2})\lt \infty$, 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.
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