Geodesic
On~the~theory of nonselfadjoint operators of Schr\"odinger type with a matrix potential
Izvestiya. Mathematics , Tome 41 (1993) no. 2, pp. 193-205.

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The author studies the theory of dilation, characteristic function, and spectral analysis of dissipative operators of Schrödinger type with a matrix potential in $L_2((0,\infty);E)$ which are an extension of a minimal symmetric operator with defect indices $(2n,2n)$ $(\dim E=n\infty)$. 
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B. P. Allakhverdiev. On~the~theory of nonselfadjoint operators of Schr\"odinger type with a matrix potential. Izvestiya. Mathematics , Tome 41 (1993) no. 2, pp. 193-205. http://geodesic.mathdoc.fr/item/IM2_1993_41_2_a1/

[1] Sekefalvi-Nad V., Foyash Ch., Garmonicheskii analiz operatorov v gilbertovom prostranstve, Mir, M., 1970 | MR

[2] Pavlov V. S., “Teoriya dilatatsii i spektralnyi analiz nesamosopryazhennykh differentsialnykh operatorov”, Teoriya operatorov v lineinykh prostranstvakh, Tr. 7-oi zimnei shkoly (Drogobych, 1974), M., 1976, 3–69 | Zbl

[3] Pavlov B. S., “Ob usloviyakh otdelimosti spektralnykh komponent dissipativnogo operatora”, Izv. AN SSSR. Ser. matem., 39:1 (1975), 123–148 | MR | Zbl

[4] Pavlov V. S., “Samosopryazhennaya dilatatsiya dissipativnogo operatora Shredingera i razlozhenie po ego sobstvennym funktsiyam”, Matem. sb., 102(144):4 (1977), 511–536 | MR | Zbl

[5] Nikolskii N. K., Lektsii ob operatore sdviga, Nauka, M., 1980 | MR

[6] Laks P., Fillips R., Teoriya rasseyaniya, Mir, M., 1971 | MR

[7] Allakhverdiev B. P., “O dissipativnykh rasshireniyakh simmetricheskogo operatora Shredingera v sluchae predelnogo kruga Veilya”, DAN SSSR, 293:4 (1987), 777–781 | MR | Zbl

[8] Allakhverdiev B. P., “K teorii dilatatsii i spektralnomu analizu dissipativnykh operatorov Shredingera v sluchae predelnogo kruga Veilya”, Izv. AN SSSR. Ser. matem., 54:2 (1990), 242–257 | MR

[9] Lidskii V. B., “O chisle reshenii s integriruemym kvadratom sistemy differentsialnykh uravnenii $y''+p(t)y=\lambda y$”, DAN SSSR, 95:2 (1954), 217–220 | MR | Zbl

[10] Gorbachuk V. I., Gorbachuk M. L., Granichnye zadachi dlya differentsialno-operatornykh uravnenii, Nauk. dumka, Kiev, 1984 | MR | Zbl

[11] Ronkin L. I., Vvedenie v teoriyu tselykh funktsii mnogikh peremennykh, Nauka, M., 1971 | MR | Zbl

[12] Ginzburg Yu. P., Telyush N. A., “Ob isklyuchitelnykh mnozhestvakh analiticheskikh matrits-funktsii, szhimayuschikh i dissipativnykh operatorov”, Izv. vyssh. uchebnykh zavedenii. Matematika, 267:8 (1984), 9–14 | MR | Zbl

[13] Gorbachuk M. L., “O spektralnykh funktsiyakh differentsialnogo uravneniya vtorogo poryadka s operatornymi koeffitsientami”, Ukr. matem. zhurn., 18:2 (1966), 3–21 | MR | Zbl

[14] Atkinson F. V., Diskretnye i nepreryvnye granichnye zadachi, Mir, M., 1968 | MR | Zbl