Geodesic
Recovery of nonselfadjoint differential operators on the half-line from the Weyl matrix
Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 413-438 Cet article a éte moissonné depuis la source Math-Net.Ru

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The inverse problem of recovering differential operators $$ ly=y^{(n)}+\sum_{\nu=0}^{n-2}p_\nu(x)y^{(\nu)}, \qquad x>0, $$ from the Weyl matrix is investigated. A solution of this problem is given for arbitrary behavior of the spectrum, along with necessary and sufficient conditions and a uniqueness theorem. 
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     author = {V. A. Yurko},
     title = {Recovery of nonselfadjoint differential operators on the half-line from the {Weyl} matrix},
     journal = {Sbornik. Mathematics},
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     year = {1992},
     volume = {72},
     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/SM_1992_72_2_a8/}
}
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V. A. Yurko. Recovery of nonselfadjoint differential operators on the half-line from the Weyl matrix. Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 413-438. http://geodesic.mathdoc.fr/item/SM_1992_72_2_a8/

[1] Marchenko V. A., Spektralnaya teoriya operatorov Shturma-Liuvillya, Naukova dumka, Kiev, 1972 | MR | Zbl

[2] Levitan B. M., Obratnye zadachi Shturma-Liuvillya, Nauka, M., 1984 | MR

[3] Marchenko V. A., “Nekotorye voprosy teorii differentsialnogo operatora vtorogo poryadka”, DAN SSSR, 72:3 (1950), 457–460 | MR | Zbl

[4] Gelfand I. M., Levitan B. M., “Ob opredelenii differentsialnogo uravneniya po ego spektralnoi funktsii”, Izv. AN SSSR. Ser. matem., 15 (1951), 309–360 | MR | Zbl

[5] Fage M. K., “Integralnye predstavleniya operatorno-analiticheskikh funktsii odnoi nezavisimoi peremennoi”, Tr. MMO, 8 (1959), 3–48 | MR | Zbl

[6] Leontev A. F., “Otsenka rosta resheniya odnogo differentsialnogo uravneniya”, SMZh, 1:3 (1960), 456–487 | MR

[7] Sakhnovich L. A., “Metod operatora preobrazovaniya dlya uravnenii vysshikh poryadkov”, Matem. sb., 55(97) (1961), 347–360 | Zbl

[8] Khachatryan I. G., “O edinstvennosti vosstanovleniya differentsialnogo operatora s analiticheskimi koeffitsientami po ego spektralnoi matritse-funktsii”, DAN ArmSSR, 71:2 (1980), 91–97 | MR | Zbl

[9] Khachatryan I. G., “O nekotorykh obratnykh zadachakh dlya differentsialnykh operatorov vysshikh poryadkov na poluosi”, Funktsion. analiz i ego pril., 17:1 (1983), 40–52 | MR | Zbl

[10] Khachatryan I. G., “Ob odnoi obratnoi zadache dlya differentsialnykh operatorov vysshikh poryadkov na vsei osi”, Izv. AN ArmSSR. Ser. matem., 18:5 (1983), 394–402 | MR | Zbl

[11] Deift P., Tomei C., Trubowitz E., “Inverse Scattering and the Boussinesq Equation”, Comm. Pure Appl. Math., 35 (1982), 567–628 | DOI | MR | Zbl

[12] Beals R., “The inverse problem for ordinary differential operators on the line”, Amer. J. Math., 107:2 (1985), 281–366 | DOI | MR | Zbl

[13] Sukhanov V. V., “Obratnaya zadacha dlya samosopryazhennogo differentsialnogo operatora na osi”, Matem. sb., 137(179) (1988), 242–259 | Zbl

[14] Leibenzon Z. L., “Obratnaya zadacha spektralnogo analiza dlya differentsialnykh operatorov vysshikh poryadkov”, Tr. MMO, 15 (1966), 70–144 | MR | Zbl

[15] Leibenzon Z. L., “Spektralnye razlozheniya otobrazhenii sistem kraevykh zadach”, Tr. MMO, 25 (1971), 15–58 | MR | Zbl

[16] Baranova E. A., “O vosstanovlenii differentsialnykh operatorov vysshikh poryadkov po ikh spektram”, DAN SSSR, 205:6 (1972), 1271–1273 | MR | Zbl

[17] Yurko V. A., “O vosstanovlenii differentsialnykh operatorov chetvertogo poryadka”, Differents. uravneniya, 19:11 (1983), 2016–2017 | MR

[18] Yurko V. A., “Edinstvennost vosstanovleniya dvuchlennykh differentsialnykh operatorov po dvum spektram”, Matem. zametki, 43:3 (1988), 356–364 | MR

[19] Yurko V. A., Obratnaya zadacha dlya differentsialnykh operatorov, Dep. v VINITI 22.03.89, No1859-v 89, Sarat. gos. un-t, Saratov, 1989 | MR

[20] Pavlov B. S., “O nesamosopryazhennom operatore na poluosi”, DAN SSSR, 141:4 (1961), 807–810 | Zbl

[21] Pavlov B. S., “K spektralnoi teorii nesamosopryazhennykh differentsialnykh operatorov”, DAN SSSR, 146:2 (1962), 1267–1270

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

[23] Stepanov V. V., Kurs differentsialnykh uravnenii, Fizmatgiz, M., 1959 | Zbl

[24] Privalov I. I., Vvedenie v teoriyu funktsii kompleksnogo peremennogo, Nauka, M., 1967 | MR

[25] Gakhov F. D., Kraevye zadachi, Nauka, M., 1977 | MR