Extensions of symmetric Schrodinger operators with matrix potentials
Izvestiya. Mathematics , Tome 59 (1995) no. 1, pp. 45-62.

Voir la notice de l'article provenant de la source Math-Net.Ru

A space of boundary values is constructed for symmetric Schrodinger operators with matrix potentials on the half-line and on the whole line. A description of all maximal dissipative, self-adjoint and other extensions of such operators is given in terms of boundary conditions.
@article{IM2_1995_59_1_a1,
     author = {B. P. Allakhverdiev},
     title = {Extensions of symmetric {Schrodinger} operators with matrix potentials},
     journal = {Izvestiya. Mathematics },
     pages = {45--62},
     publisher = {mathdoc},
     volume = {59},
     number = {1},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_59_1_a1/}
}
TY  - JOUR
AU  - B. P. Allakhverdiev
TI  - Extensions of symmetric Schrodinger operators with matrix potentials
JO  - Izvestiya. Mathematics 
PY  - 1995
SP  - 45
EP  - 62
VL  - 59
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1995_59_1_a1/
LA  - en
ID  - IM2_1995_59_1_a1
ER  - 
%0 Journal Article
%A B. P. Allakhverdiev
%T Extensions of symmetric Schrodinger operators with matrix potentials
%J Izvestiya. Mathematics 
%D 1995
%P 45-62
%V 59
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1995_59_1_a1/
%G en
%F IM2_1995_59_1_a1
B. P. Allakhverdiev. Extensions of symmetric Schrodinger operators with matrix potentials. Izvestiya. Mathematics , Tome 59 (1995) no. 1, pp. 45-62. http://geodesic.mathdoc.fr/item/IM2_1995_59_1_a1/

[1] Neuman J.von, “Allgemenice Eigenwerttheorie Hermitischer Funktional operatoren”, Math. Ann., 102 (1929), 49–131 | DOI | Zbl

[2] Weyl H., “Über gewohnliche Differentialgleichungen mit Singularitaten und die zugehorigen Entwicklungen willkurlicher Funktionen”, Math. Ann., 68 (1910), 222–269 | DOI | MR

[3] Stone M. H., Linear transformations in Hilbert space and their applications to analysis, Amer. Math. Soc. Colloquium Public., Providence, 15, New York, 1932 | MR | Zbl

[4] Rellich F., “Halbbeschränkte gewöhnliche Differentialoperatoren zweiter Ordnung”, Math. Ann., 122 (1951), 343–368 | DOI | MR | Zbl

[5] Krein M. G., “Teoriya samosopryazhennykh rasshirenii poluogranichennykh operatorov i ee prilozheniya. I; II”, Matem. sb., 20:3 (1947), 431–495 | MR | Zbl

[6] Krein M. G., “O neopredelennom sluchae kraevoi zadachi Shturma–Liuvillya v intervale $(0,\infty)$”, Izv. AN SSSR. Ser. matem., 16:4 (1952), 293–324 | MR | Zbl

[7] Vishik M. I., “Ob obschikh kraevykh zadachakh dlya ellipticheskikh differentsialnykh uravnenii”, Tr. MMO, 1, URSS, M., 1952, 187–246 | MR

[8] Birman M. Sh., “K teorii samosopryazhennykh rasshirenii polozhitelno opredelennykh operatorov”, Matem. sb., 38:4 (1956), 431–450 | MR | Zbl

[9] Fillips R. S., “Dissipativnye operatory i giperbolicheskie sistemy differentsialnykh uravnenii v chastnykh proizvodnykh”, Matematika, 6:4 (1962), 11–70

[10] Rofe-Beketov F. S., “O samosopryazhennykh rasshireniyakh differentsialnykh operatorov v prostranstve vektor-funktsii”, Teoriya funktsii, funkts. analiz i ikh prilozh., 1969, no. 8, 3–24 | MR | Zbl

[11] Rofe-Beketov F. S., “Samosopryazhennye rasshireniya differentsialnykh operatorov v prostranstve vektor-funktsii”, DAN SSSR, 184:5 (1969), 1034–1037 | MR | Zbl

[12] Gorbachuk V. I., Gorbachuk M. L., “O spektre samosopryazhennykh rasshirenii minimalnogo operatora, porozhdennogo vyrazheniem Shturma–Liuvillya s operatornym potentsialom”, Ukr. matem. zhurn., 24:6 (1972), 726–734 | MR | Zbl

[13] Gorbachuk M. L., “Samosopryazhennye granichnye zadachi dlya differentsialnogo uravneniya vtorogo poryadka s neogranichennym operatornym koeffitsientom”, Funkts. analiz i ego prilozh., 5:1 (1971), 10–21 | MR | Zbl

[14] Bairamogly M., “O samosopryazhennykh rasshireniyakh operatornogo uravneniya s osobennostyu”, Izv. AN Azerb.SSR. Ser. fiz.-tekhn. i matem. nauk, 1976, no. 2, 140–143 | MR | Zbl

[15] Kholkin A. M., “Samosopryazhennye kraevye usloviya na beskonechnosti dlya kvaziregulyarnoi sistemy differentsialnykh uravnenii chetnogo poryadka”, Teor. operat. v funkts. prost. i ee prilozh., Kiev, 1981, 174–183 | MR | Zbl

[16] Gorbachuk M. L., Kochubei A. N., Rybak M. A., “Dissipativnye rasshireniya differentsialnykh operatorov v prostranstve vektor-funktsii”, DAN SSSR, 205:5 (1972), 1029–1032 | MR | Zbl

[17] Kochubei A. N., “O rasshireniyakh simmetricheskikh operatorov i simmetricheskikh binarnykh otnoshenii”, Matem. zametki, 17:1 (1975), 41–48 | MR

[18] Bruk V. M., “Ob odnom klasse kraevykh zadach so spektralnym parametrom v granichnom uslovii”, Matem. sb., 100:2 (1976), 210–216 | MR | Zbl

[19] Gorbachuk M. L., Mikhailets V. A., “Poluogranichennye samosopryazhennye rasshireniya simmetricheskikh operatorov”, DAN SSSR, 226:4 (1976), 765–768 | MR

[20] Kuzhel A. V., “Pravilnye rasshireniya ermitovykh operatorov”, DAN SSSR, 251:1 (1980), 30–33 | MR | Zbl

[21] Kochubei A. N., “Ellipticheskie operatory s granichnymi usloviyami na podmnozhestve mery nul”, Funkts. analiz i ego prilozh., 16:2 (1982), 78–79 | MR

[22] Mikhailets V. A., “Spektry operatorov i granichnye zadachi”, Spektralnyi analiz diff. oper., Kiev, 1980, 106–131 | MR

[23] Vainerman L. I., “O rasshireniyakh zamknutykh operatorov v gilbertovom prostranstve”, Matem. zametki, 28:6 (1980), 833–841 | MR

[24] Lyantse V. E., Storozh O. G., Metody teorii neogranichennykh operatorov, Nauk. dumka, Kiev, 1983 | MR

[25] Gorbachuk V. I., Gorbachuk M. L., Kochubei A. N., “Teoriya rasshireniya simmetricheskikh operatorov i granichnye zadachi dlya differentsialnykh uravnenii”, Ukr. matem. zhurn., 41:10 (1989), 1299–1312 | MR

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

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