\((0,m)\) Pál-type interpolation on the Möbius transform of roots of unity
Let \(n,m>1\) be integers and let \(\alpha\) be a complex number such that \(\alpha^2,\alpha^m,\alpha^m,\) \(\alpha^{n+m}\not=1\). For \(k=n\) or \(k=n+m\), consider the complex polynomials \(w_k(z)=(z+\alpha)^k-(1+\alpha z)^k\). The main result is: the \((0,m)\)-Pál-type interpolation problem on the zeros of the pair \(\{w_{n+m}(z),w_n(z)\}\) is regular, i.e. there is a unique complex polynomial \(P(z)\) of degree \(2n+m-1\) which take prescribed values at the zeros of \(w_{n+m}\) and prescribed values of the \(m\)th derivative of \(P(z)\) at the zeros of \(w_n\).
scientific article; zbMATH DE number 2157665