Geodesic
On a transformation operator for a system of Sturm--Liouville equations
Matematičeskie zametki, Tome 11 (1972) no. 5, pp. 559-567.

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We prove the existence of a transformation operator with a condition at infinity that sends a solution of the matrix equation $-y''+My=\lambda^2y$ ($M$ is a constant Hermitian matrix) into a solution of the matrix equation $-y''+Q(x)y+My=\lambda^2y$ (the matrix function $Q(x)$ is continuously differentiable for $0\leqslant x\infty$ and it is Hermitian for each $x$ belonging to $[0,\infty)$); we study some properties of the kernel of the transformation operator. 
@article{MZM_1972_11_5_a10,
     author = {M. B. Veliev and M. G. Gasymov},
     title = {On a transformation operator for a system of {Sturm--Liouville} equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {559--567},
     publisher = {mathdoc},
     volume = {11},
     number = {5},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a10/}
}
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M. B. Veliev; M. G. Gasymov. On a transformation operator for a system of Sturm--Liouville equations. Matematičeskie zametki, Tome 11 (1972) no. 5, pp. 559-567. http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a10/