On the multiple Nevanlinna-Pick matrix interpolation in the class imagep and the Carathéodory matrix coefficient problem Original Research Article

In the present paper an intrinsic one-to-one correspondence between the (finite) multiple Nevanlinna-Pick matrix interpolation (NP) problem in the Carathéodory class and the Carathéodory matrix coefficient (CC) problem (or, equivalently, the truncated trigonometric matrix moment (TM) problem) is established. Thanks to this correspondence, the NP problem is reduced to what amounts to solving the CC problem (or the TM problem) associated with the so-called Toeplitz block-vector of the former in both the nondegenerate and degenerate cases simultaneously.