A characterization of intermediate Weyl coefficients
We denote by \(N_0\) the class of all analytic functions \(q\) (called Nevanlinna functions) defined on the non-real complex plane \(\mathbb{C} \setminus \mathbb{R}\) such that \(\overline{q (\overline z)}=q(z)\) and \(q\) maps the upper halfplane into itself. In an earlier work of \textit{H. Woracek} [Integral Equ. Oper. Theory 37, 238-249 (2000; Zbl 0957.46019)] the subclass \(N_{0/0}\) of \(N_0\) was defined, and a criterion for \(q\in N_{0/0}\) was given in terms of the poles and residues of \(q\). In the present paper, the subclass \(N_{0/ \Delta}\) of \(N_0\) (motivated by applications to canonical systems of differential equations) is defined for each integer \(\Delta>0\), as follows. Each \(q\in N_0\) generates a recursive sequence \(\{q_ik\}\) in which \(q_0=q\) and \(q_{k+1} (z)=-1/(q_k(z) -1/z)\). We define \(q\in N_{0/ \Delta}\) in case \(\Delta\) is the least integer such that \(q_\Delta\in N_{0/0}\). The authors derive a criterion for \(q\in N_{0/ \Delta}\) in terms of the poles and residues of \(q\).
scientific article; zbMATH DE number 1753103