Geodesic
Spectral Theory of a Class of Canonical Differential Systems
Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 2, pp. 50-62.

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The general spectral theory of canonical systems is used to study a generalized Krein system. Direct and inverse problems for this system are considered. In particular, some proofs are supplied for Krein's results published by him without proof. 
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L. A. Sakhnovich. Spectral Theory of a Class of Canonical Differential Systems. Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 2, pp. 50-62. http://geodesic.mathdoc.fr/item/FAA_2000_34_2_a5/

[1] Krein M. G., “Kontinualnye analogi predlozhenii o mnogochlenakh, ortogonalnykh na edinichnoi okruzhnosti”, DAN SSSR, 105:4 (1955), 637–640 | MR | Zbl

[2] Sakhnovich L. A., “On one class of canonical systems on half-axis”, Integral Equations Operator Theory, 31:1 (1998), 92–112 | DOI | MR | Zbl

[3] Sakhnovich L. A., Spectral Theory of Canonical Differential Systems. Method of Operator Identities, Operator Theory, Advances and Applications, 107, Birkhäuser Verlag, Basel, 1999 | MR | Zbl

[4] Potapov V. P., “Multiplikativnaya struktura $j$-nerastyagivayuschikh matrits-funktsii”, Trudy MMO, 4, 1955, 125–236 | MR | Zbl

[5] Levitan B. M., Obratnye zadachi Shturma–Liuvillya, Nauka, M., 1984 | MR

[6] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, GITTL, M.-L., 1950 | MR

[7] Rozanov Yu. A., Statsionarnye sluchainye protsessy, Fizmatgiz, 1963 | MR

[8] Ginzburg Yu. P., “Multiplikativnye predstavleniya operator-funktsii ogranichennogo vida”, UMN, 22:1 (1967), 163–165 | MR

[9] Ginzburg Yu. P., Shevchuk L. V., “On the Potapov theory of multiplicative representations”, Operator Theory, Advances and Appl., 72, Birkhäuser Verlag, 1994, 28–47 | MR | Zbl

[10] Sakhnovich L. A., “Dissipativnye operatory s absolyutno nepreryvnym spektrom”, Trudy MMO, 19, 1968, 211–270 | MR | Zbl