A recent overview with pointers to the literature is Complex B-splines, by Forster, Blu, and Unser; see page 262.

One of the early contributions is Complex Cubic Splines, by Ahlberg, Nelson, and Walsh.

A monograph on this topic, German, is Spline-Funktionen in Komplexen by Walz.

An overview with pointers to the literature is Complex B-splines, by Forster, Blu, and Unser; see page 262.

One recent application is Parameter characterization of complex wavelets and its use in 3D reconstruction, by Lopez et al.