Does anyone know any results regarding existence of a solution to a Birkhoff interpolation problem at complex points? In particular, are there conditions for when there exists a real polynomial $p(x)$ satisfying $p(x_j)=c_j$ for $x_j\in\mathbb{R}$ and $p^{(k)}(z_j)=b_{jk}$ for $k=1,2$ and $z_j\in \mathbb{C}$? I have seen a paper by Ferguson discussing uniqueness, but I am more interested in existence.
Thanks in advance!
