Abstract
A regularized trace formula of first order for the matrix Sturm-Liouville operator \(-\frac{d^2}{dx^2}+Q\) with a \(d\times d\) self-adjoint matrix-valued potential \(Q\) in \(L^2((0,\pi );dx)^d\) is derived, which extends the well-known scalar case \(d=1\).
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