Geodesic
Analytic theory of a~class of interpolation problems
Izvestiya. Mathematics , Tome 22 (1984) no. 3, pp. 419-463.

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This paper studies a method of solving the matrix Nevanlinna–Pick, Carathéodory, and Hamburger problems by using the theory of analytic $J$-expanding matrix-valued functions ($J$-theory). The solution of each problem is represented as a linear fractional transformation whose coefficient matrix is an entity of $J$-theory. Bibliography: 11 titles. 
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I. V. Kovalishina. Analytic theory of a~class of interpolation problems. Izvestiya. Mathematics , Tome 22 (1984) no. 3, pp. 419-463. http://geodesic.mathdoc.fr/item/IM2_1984_22_3_a1/

[1] Potapov V. P., “Multiplikativnaya struktura $J$-nerastyagivayuschikh matrits-funktsii”, Tr. Mosk. mat. ob-va, 4, 1955, 125–236 | MR | Zbl

[2] Efimov A. V., Potapov V. P., “$J$-rastyagivayuschie matritsy-funktsii i ikh rol v analiticheskoi teorii elektricheskikh tsepei”, UMN, 28:1(169) (1973), 65–130 | MR | Zbl

[3] Kovalishina I. V., “Additivnoe razlozhenie proizvolnoi reaktivnoi matritsy-funktsii”, Izv. AN Arm. SSR, 6:1 (1971), 43–60 | MR | Zbl

[4] Orlov S. A., “Gnezdyaschiesya matrichnye krugi, analiticheski zavisyaschie ot parametra, i teoremy invariantnosti rangov radiusov predelnykh matrichnykh krugov”, Izv. AN SSSR. Ser. matem., 40:3 (1976), 593–644 | MR | Zbl

[5] Kovalishina I. V., Potapov V. P., “Indefinitnaya metrika v probleme Nevanlinny–Pika”, DAN Arm. SSR, 59:1 (1974), 17–22 | MR | Zbl

[6] Akhiezer N. I., Klassicheskaya problema momentov i nekotorye voprosy analiza, svyazannye s neyu, Nauka, M., 1961

[7] Löwner K., “Über monotone Matrixfunktionen”, Math. Zeitschr., 38 (1934), 177–216 | DOI | MR | Zbl

[8] Schur I., “Über Potenzreihen, die in Innern des Einheitskreises beschränkt sind”, Journ. für Reine und Angew. Math., 147 (1917), 205–232; 148 (1918), 122–145 | Zbl

[9] Riesz M., “Sur le probleme des moments, I, II, III”, Ark. Mat. Astr. Fys., 16 (1921), 38–90

[10] Denjov A., “Sur une classe de fonctions analytiques”, Comptes Rendus, 188 (1929), 108–140

[11] Nevanlinna R., “Über beschränkte analytische Funktionen”, Ann. Acad. Sci. Fenn., 32 (1929), 1–75