Geodesic
Hilbert problem with unitary coefficient matrix
Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 2, pp. 184-191

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For the Hilbert problem with unitary matrix-valued coefficient function $G(t)$ a solution is obtained in the form of a series whose general term can be found by quadrature from $G(t)$. Sufficient conditions are determined for the convergence of this series, establishing the dependence of the rate of convergence on the “proximity” of $G(t)$ to the class of matrices of diagonal form, for which the Hilbert problem admits analytic solution in quadratures. The obtained solutions are used to construct the Jost matrix of the coupled $^3S_1+{^3D_1}$ partial channels of $np$ scattering. 
@article{TMF_1984_58_2_a2,
     author = {V. M. Muzafarov},
     title = {Hilbert problem with unitary coefficient matrix},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {184--191},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_58_2_a2/}
}
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V. M. Muzafarov. Hilbert problem with unitary coefficient matrix. Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 2, pp. 184-191. http://geodesic.mathdoc.fr/item/TMF_1984_58_2_a2/