The degenerate Carath\'eodory problem and the elementary multiple factor
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 1 (2005), pp. 225-244

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The degenerate matricial interpolation Carathéodory problem is solved. To solve this problem we use the V. P. Potapov's approach based on the theory of $J$-expansive matrix-functions. The $\mathcal K$-type subspace technique also plays an important role in these investigations.
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     author = {N.N. Chernovol},
     title = {The degenerate {Carath\'eodory} problem and the elementary multiple factor},
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N.N. Chernovol. The degenerate Carath\'eodory problem and the elementary multiple factor. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 1 (2005), pp. 225-244. http://geodesic.mathdoc.fr/item/JMAG_2005_1_a5/