We give a new treatment of Quiggin’s and McCullough’s characterization of complete Nevanlinna-Pick kernels. We show that a kernel has the matrix-valued NevanlinnaPick property if and only if it has the vector-valued Nevanlinna-Pick property. We give a representation of all complete Nevanlinna-Pick kernels, and show that they are all restrictions of a universal complete Nevanlinna-Pick kernel.

In this paper, we present the LMI conditions to characterize the strictly bounded realness of the state-space realization of the solution to the bi-tangential rational interpolation problem, i.e., they give the solution to the bitangential Nevanlinna-Pick interpolation problem [13], [3]. The bi-tangential Nevanlinna-Pick interpolation problem is the generalization of the classical interpolation...

Cartan’s method is used to prove a several variable, non-Archimedean, Nevanlinna Second Main Theorem for hyperplanes in projective space. The corresponding defect relation is derived, but unlike in the complex case, we show that there can only be finitely many non-zero non-Archimedean defects. We then address the non-Archimedean Nevanlinna inverse problem, by showing that given a set of defects...