Geodesic
Defect indices of $J_m$-matrices and of differential operators with polynomial coefficients
Sbornik. Mathematics, Tome 14 (1971) no. 4, pp. 471-500

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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. 
@article{SM_1971_14_4_a1,
     author = {A. L. Chistyakov},
     title = {Defect indices of $J_m$-matrices and of differential operators with polynomial coefficients},
     journal = {Sbornik. Mathematics},
     pages = {471--500},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_14_4_a1/}
}
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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/