We consider the Schrödinger operator on the halfline with the potential \((m^2-\frac{1}{4})\frac{1}{x^2}\), often called the Bessel operator. We assume that m is complex. We study the domains of various closed homogeneous realizations of the Bessel operator. In particular, we prove that the domain of its minimal realization for \(|\mathrm{Re}(m)|<1\) and of its unique closed realization for \(\mathrm{Re}(m)>1\) coincide with the minimal second-order Sobolev space. On the other hand, if \(\mathrm{Re}(m)=1\) the minimal second-order Sobolev space is a subspace of infinite codimension of the domain of the unique closed Bessel operator. The properties of Bessel operators are compared with the properties of the corresponding bilinear forms.

我们认为半线上的Schrödinger算子具有\（（m ^ 2- \ frac {1} {4}）\ frac {1} {x ^ 2} \的势能，通常被称为Bessel算子。我们假设m是复数。我们研究了Bessel算子的各种封闭齐次实现的域。特别是，我们证明了其最小实现对的域\（| \ mathrm {重新}（M）| <1 \）其独特的封闭实现为和\（\ mathrm {重新}（米）> 1 \）与最小二阶Sobolev空间一致。另一方面，如果\（\ mathrm {Re}（m）= 1 \）最小二阶Sobolev空间是唯一闭合Bessel算子的域的无穷维子空间。将Bessel算子的性质与相应的双线性形式的性质进行比较。