On deficiency indices of singular operators of odd order (Q869750)

The paper examines differential operators of the form \[ \begin{multlined} ly=(-1)^n2iy^{(2n+1)}+\sum^n_{k=0}(-1)^k(p_{n-k} (x)y^{(k)})^{(k)}+\\ +i\sum^{n-1}_{j=0}(-1)^j[(q_{n-j}(x) y^{(j)})^{(j+1)}+(q_{n-j}(x)y^{(j+1)})^{(j)}]=i\sigma y, \end{multlined} \] with \(p_k(x)\) and \(q_i(x)\) given by some series. Denote by \(L_0\) the minimal differential operator generated by the operator \(1_y\) in the space \(L^2(0,\infty)\). Under certain additional conditions on the data, it is proven that the deficiency indices of the operator \(L_0\) are either \((n,n+1)\) or \((n+1,n)\).