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- W2266580147 abstract "Let $A_j,B_j$ $(j=0,1,ldots)$ be $m times m$ matrices, whose elements are complex numbers, $A_j$ are selfadjoint matrices and $B_j^{-1}$ exist. We study the deficiency index problem for minimal closed symmetric operator $L$ with domain $D_L$, generated by the Jacobi matrix $textbf{J}$ with entries $A_j,B_j$ in the Hilbert space $l_m^2$ of sequences $ u=(u_0,u_1, ldots), u_j in C^m$ by mapping $u rightarrow textbf{J}u$, i.e. by the formula $Lu=lu$ for $u in D_L$, where $lu=((lu)_0,(lu)_1, ldots)$ and $$ (lu)_0:=A_0u_0+B_0u_1, quad (lu)_j:=B^*_{j-1}u_{j-1}+A_ju_j+B_ju_{j+1}, ;; j=1,2, ldots $$ It is well known that the case of the minimal deficiency numbers of the operator $L$ corresponds to the determinate case, and the case of the maximal deficiency numbers of this operator corresponds to the completely indeterminate case of the matrix power moment problem. In this paper we obtain new conditions of the minimal, maximal and not maximal deficiency numbers of the operator $L$ in terms of the entries of the matrix $textbf{J}$. The special attention is paid to the case $m=1$, i.e. we present some conditions on the elements of the numerical tridiagonal Jacobi matrix, which ensure the realization of the determinate case of the classical power moment problem." @default.
- W2266580147 created "2016-06-24" @default.
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- W2266580147 date "2015-11-28" @default.
- W2266580147 modified "2023-09-27" @default.
- W2266580147 title "Deficiency numbers of operators generated by infinite Jacobi matrices" @default.
- W2266580147 cites W2963697235 @default.
- W2266580147 doi "https://doi.org/10.48550/arxiv.1511.08950" @default.
- W2266580147 hasPublicationYear "2015" @default.
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