Geodesic
Examples of block Jacobi matrices generating symmetric operators with arbitrary possible values of the deficiency numbers
Sbornik. Mathematics, Tome 201 (2010) no. 12, pp. 1791-1800 Cet article a éte moissonné depuis la source Math-Net.Ru

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Examples of symmetric block Jacobi matrices generating symmetric operators with arbitrary possible values of the deficiency numbers are constructed for the first time. Explicit formulae for the bases of the deficiency subspaces are presented. Bibliography: 7 titles.
Keywords: symmetric block Jacobi matrices, symmetric operators, deficiency subspaces, deficiency numbers. 
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Yu. M. Dyukarev. Examples of block Jacobi matrices generating symmetric operators with arbitrary possible values of the deficiency numbers. Sbornik. Mathematics, Tome 201 (2010) no. 12, pp. 1791-1800. http://geodesic.mathdoc.fr/item/SM_2010_201_12_a3/

[1] M. G. Krein, “Beskonechnye $J$ matritsy i matrichnaya problema momentov”, Dokl. AN SSSR, 69:3 (1949), 125–128 | MR | Zbl

[2] M. G. Krein, “Fundamental aspects of the representation theory of Hermitian operators with deficiency index ($m,m$)”, Amer. Math. Soc. Transl. 2, 97 (1971), 75–143 | MR | Zbl

[3] Yu. M. Berezans'kiǐ, Expansions in eigenfunctions of selfadjoint operators, Amer. Math. Soc., Providence, RI, 1968 | MR | MR | Zbl | Zbl

[4] V. I. Kogan, “Ob operatorakh, porozhdennykh $l_p$-matritsami v sluchae maksimalnykh indeksov defekta”, Teoriya funktsii, funkts. analiz i ikh pril., 1970, no. 11, 103–107 | MR | Zbl

[5] A. G. Kostyuchenko, K. A. Mirzoev, “Complete indefiniteness tests for Jacobi matrices with matrix entries”, Funct. Anal. Appl., 35:4 (2001), 265–269 | DOI | MR | Zbl

[6] Yu. M. Dukarev, “Deficiency numbers of symmetric operators generated by block Jacobi matrices”, Sb. Math., 197:8 (2006), 1177–1203 | DOI | MR | Zbl

[7] I. V. Kovalishina, V. P. Potapov, “Radiusy kruga Veilya v matrichnoi zadache Nevanlinny–Pika”, Teoriya operatorov v funktsionalnykh prostranstvakh i ee prilozheniya, Naukova dumka, Kiev, 1981, 25–49 | MR | Zbl