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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.
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