the recent IWOTA meetings, IWOTA 2006 was focused on a few special themes, without loss of the general IWOTA mission. Our special interest areas were Hilbert/Krein space operator theory; Complex function theory related to Hilbert space operators; Systems theory related to Hilbert space operators. This volume contains 16 contributions, which re?ect the recent development in operator theory and applications. The organizers gratefully acknowledge the support of the following institutions: KRF (Korea Research Foundation); Department of Mathematics, Seoul National University; Research Institute of Mathematics, Seoul National University. Tsuyoshi Ando, Raul ' Curto Il Bong Jung, Woo Young Lee (Editors) OperatorTheory: Advances andApplications,Vol.187, 1-16 c 2008Birkh. auserVerlagBasel/Switzerland AConnectionbetweenSzegoandNehari SequencesintheMatrix-valuedCase Daniel Alpay and Israel Gohberg Abstract. One can associate to a rational function which is moreover strictly positive on the unit circle two sequences of numbers in the open unit disk, called the Szeg. o sequence and the Nehari sequence. In the scalar case, they coincide up to multiplication by?1. We study the corresponding result in the matrix-valued case. Mathematics Subject Classi?cation (2000). Primary: 34A55, 49N45, 70G30; Secondary: 93B15, 47B35. Keywords. Inverse problems, scattering matrix, Schurparameters, state space method, extension problems. 1. Introduction Letw(z) be a scalar rational function strictly positive on the unit circle. One can associate to it an in?nite sequence of numbers in the open unit disk, called in [1] a Szeg. o sequence. This sequence characterizes in a unique wayw(z)providedsome normalization is chosen; we will take 2? 1 it w(e )dt=1.

These papers from the Workshop on Operator Theory and Complex Analysis review advances in operator theory and complex analysis, and their interplay in applications to mathematical system theory and control. Special attention is paid to different extension and interpolation problems for matrix and operator valued functions. Other topics include: operator inequalities and operator means; matrix completion problems; operators in spaces with indefinite scalar products and non-selfadjoint operators; and scattering and inverse spectral problems. The book should be useful to both pure and applied mathematicians.