Geodesic
Deficiency numbers of symmetric operators generated
Sbornik. Mathematics, Tome 197 (2006) no. 8, pp. 1177-1203 
Yu. M. Dyukarev. Deficiency numbers of symmetric operators generated. Sbornik. Mathematics, Tome 197 (2006) no. 8, pp. 1177-1203. http://geodesic.mathdoc.fr/item/SM_2006_197_8_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Symmetric block Jacobi matrices $J$ and the corresponding symmetric operators $L$ are studied. Let $m$ be the size of the blocks in the matrix $J$. As is known, the deficiency numbers $m_+$ and $m_-$ of the operator $L$ satisfy the inequalities $0\leqslant m_+,m_-\leqslant m$ and achieve their maximum value $m$ simultaneously. Let $m_+$ and $m_-$ be arbitrary integers such that $0\leqslant m_+,m_-\leqslant m-1$. It is shown that there exists a symmetric Jacobi matrix $J$ such that $m_+$ and $m_-$ are the deficiency numbers of the corresponding symmetric operator $L$. Bibliography: 13 titles.

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