Geodesic
Defect indices of $J_m$-matrices and of differential operators with polynomial coefficients
Sbornik. Mathematics, Tome 14 (1971) no. 4, pp. 471-500 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of the defect indices of the symmetric operator $C$ which acts on the space $l_2$ and is generated by a regular Hermitian $J_m$-matrix with increasing elements is investigated. The asymptotics, as $k\to\infty$, of the eigenvectors $U=(u_0,u_1,\dots,u_k,\dots)$ of the operator $C^*$ which correspond to the nonreal eigenvalues are obtained. The results are applied to ordinary differential operators with polynomial coefficients defined on the entire $x$-axis. Figures: 2. Bibliography: 15 titles. 
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A. L. Chistyakov. Defect indices of $J_m$-matrices and of differential operators with polynomial coefficients. Sbornik. Mathematics, Tome 14 (1971) no. 4, pp. 471-500. http://geodesic.mathdoc.fr/item/SM_1971_14_4_a1/

[1] M. G. Krein, “Beskonechnye $J$-matritsy i matrichnaya problema momentov”, DAN SSSR, 69:2 (1949), 125–128 | MR | Zbl

[2] I. M. Rapoport, O nekotorykh asimptoticheskikh metodakh v teorii differentsialnykh uravnenii, AN USSR, Kiev, 1954

[3] A. L. Chistyakov, “Beskonechnye ermitovskie matritsy s operatornymi koeffitsientami”, DAN SSSR, 178:5 (1968), 1029–1032 | Zbl

[4] A. L. Chistyakov, “Indeksy defekta simmetricheskikh differentsialnykh operatorov s polinomialnymi koeffitsientami”, DAN SSSR, 186:2 (1969), 268–271 | Zbl

[5] I. M. Glazman, Pryamye metody kachestvennogo spektralnogo analiza singulyarnykh differentsialnykh operatorov, Fizmatgiz, Moskva, 1963 | MR

[6] Yu. M. Berezanskii, “Razlozhenie po sobstvennym funktsiyam uravnenii v chastnykh raznostyakh vtorogo poryadka”, Trudy Mosk. matem. ob-va, V (1956), 203–268 | MR

[7] Yu. M. Berezanskii, Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, Naukova dumka, Kiev, 1965 | MR

[8] A. L. Chistyakov, Indeksy defekta simmetricheskikh operatorov v pryamoi summe gilbertovykh prostranstv, Kandidatskaya diss., Moskva, 1969

[9] N. G. de Brein, Asimptoticheskie metody v analize, IL, Moskva, 1961

[10] N. I. Akhiezer, Klassicheskaya problema momentov, Fizmatgiz, Moskva, 1961

[11] I. A. Vernadskii, R. A. Minlos, “Ob indeksakh defekta simmetricheskikh yakobievykh matrits”, Izv. VUZov, Matematika, 1968, no. 2(69), 16–20

[12] F. A. Berezin, Metod vtorichnogo kvantovaniya, Nauka, Moskva, 1965 | MR

[13] A. L. Chistyakov, “Indeksy defekta simmetricheskikh operatorov v pryamoi summe gilbertovykh prostranstv”, Vestnik MGU, 1969, no. 3, 15–21 | MR | Zbl

[14] M. V. Fedoryuk, “Asimptoticheskie metody v teorii odnomernykh singulyarnykh differentsialnykh operatorov”, Trudy Mosk. matem. ob-va, XV (1966), 296–345

[15] V. I. Smirnov, Kurs vysshei matematiki, t. III, ch. 2, Gostekhizdat, Moskva–Leningrad, I960