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.

In this paper, the authors study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. They first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. They propose a new notion of tensored-scalar singularity, and then answer questions on Hankel operators with matrix-valued bounded type symbols. They also examine an interpolation problem related to a certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejer Interpolation Problem for matrix rational functions. The authors then extend the $H^\infty$-functional calculus to an $\overline{H^\infty}+H^\infty$-functional calculus for the compressions of the shift. Next, the authors consider the subnormality of Toeplitz operators with matrix-valued bounded type symbols and, in particular, the matrix-valued version of Halmos's Problem 5 and then establish a matrix-valued version of Abrahamse's Theorem. They also solve a subnormal Toeplitz completion problem of $2\times 2$ partial block Toeplitz matrices. Further, they establish a characterization of hyponormal Toeplitz pairs with matrix-valued bounded type symbols and then derive rank formulae for the self-commutators of hyponormal Toeplitz pairs.