Spectral Analysis of Certain Self-Adjoint Differential Operators in a Space with Indefinite Metric
Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 568-580.

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A second-order differential operator self-adjoint with respect to an indefinite metric on the circle is considered. The spectral resolution of this operator is found. The hypergeometric function is used in the computation of the Plancherel measure.
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R. S. Ismagilov; Sh. Sh. Sultanov. Spectral Analysis of Certain Self-Adjoint Differential Operators in a Space with Indefinite Metric. Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 568-580. http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a8/

[1] Pontryagin L. S., “Ermitovy operatory v prostranstve s indefinitnoi metrikoi”, Izv. AN SSSR, 8:6 (1944), 243–280 | MR | Zbl

[2] Iokhvidov I. S., Krein M. G., “Spektralnaya teoriya operatorov v prostranstvakh s indefinitnoi metrikoi, 1”, Tr. MMO, 5, 1956, 43–72

[3] Iokhvidov I. S., Krein M. G., “Spektralnaya teoriya operatorov v prostranstvakh s indefinitnoi metrikoi, 2”, Tr. MMO, 8, 1959, 38–62

[4] Azizov T. Ya., Iokhvidov I. S., Osnovy teorii lineinykh operatorov v prostranstvakh s indefinitnoi metrikoi, Nauka, M., 1986

[5] Sultanov Sh. Sh., “O tenzornykh proizvedeniyakh predstavlenii gruppy $SL(2,\mathbb R)$”, Funktsion. analiz i ego prilozh., 10:2 (1976), 86–88 | MR

[6] Naimark M. A., “O kommutativnykh algebrakh operatorov v prostranstve $\Pi_1$”, Dokl. AN SSSR, 156:4 (1964), 734–737 | MR

[7] Gelfand I. M., Shilov G. E., Obobschennye funktsii i deistviya nad nimi, Nauka, M., 1958 | Zbl

[8] Kopson E., Asimptoticheskie razlozheniya, Mir, M., 1966

[9] Lebedev N. N., Spetsialnye funktsii i ikh prilozheniya, GIFML, L., 1963

[10] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969

[11] Starinets V. V., O nekotorykh differentsialnykh operatorakh v funktsionalnykh gilbertovykh prostranstvakh s indefinitnoi metrikoi, Dep. VINITI No 3634-84, VINITI, M., 1984