Geodesic
On dilatation theory and spectral analysis of dissipative Schrodinger operators in Weyl's limit-circle case
Izvestiya. Mathematics, Tome 36 (1991) no. 2, pp. 247-262 
B. P. Allakhverdiev. On dilatation theory and spectral analysis of dissipative Schrodinger operators in Weyl's limit-circle case. Izvestiya. Mathematics, Tome 36 (1991) no. 2, pp. 247-262. http://geodesic.mathdoc.fr/item/IM2_1991_36_2_a1/
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     author = {B. P. Allakhverdiev},
     title = {On~dilatation theory and spectral analysis of dissipative {Schrodinger} operators in {Weyl's} limit-circle case},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Dissipative Schrödinger operators are studied in Weyl's limit-circle case. A selfadjoint dilation and a spectral model of these operators are constructed and the characteristic function is computed. Theorems on the completeness of the eigenfunctions of the dissipative operators are proved.

[1] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969 | MR

[2] Titchmarsh E. Ch., Razlozheniya po sobstvennym funktsiyam, svyazannye s differentsialnymi uravneniyami vtorogo poryadka, IL, M., 1960

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

[4] Sekefalvi-Nad B., Foiash Ch., Garmonicheskii analiz operatorov v gilbertovom prostranstve, Mir, M., 1970 | MR

[5] Pavlov B. S., “Teoriya dilatatsii i spektralnyi analiz nesamosopryazhennykh differentsialnykh operatorov”, Tr. 7-i Zimnei Shkoly po matem. programmir. i smezhn. vopr., TsEMI AN SSSR, M., 1976, 3–69

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

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

[8] Katsnelson V. E., “Ob usloviyakh bazisnosti sistemy kornevykh vektorov nekotorykh klassov operatorov”, Funkts. analiz i ego prilozh., 1:2 (1967), 39–51 | MR

[9] Rofe-Beketov F. S., “Spektralnaya matritsa i obratnaya zadacha Shturma–Liuvillya na osi $(-\infty,\infty)$”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, no. 4, Kharkov, 1967, 189–197 | MR | Zbl

[10] Everitt W. N., “On a property of $m$-coefficient of a second order linear differential equation”, J. London Math. Soc., 4 (1972), 443–457 | DOI | MR | Zbl

[11] Sultanaev Ya. T., “Ob indeksakh defekta i spektra nepoluogranichennogo operatora Shturma–Liuvillya”, Dokl. AN SSSR, 276:5 (1984), 1072–1074 | MR | Zbl