TY - JOUR
T1 - The inverse problem for orthogonal Krein matrix functions
AU - Gohberg, I.
AU - Kaashoek, M.A.
AU - Lerer, L.
N1 - MR2345040
PY - 2007
Y1 - 2007
N2 - In the mid-fifties, in a seminal paper, M. G. Krein introduced continuous analogs of Szego orthogonal polynomials on the unit circle and established their main properties. In this paper, we generalize these results and subsequent results that he obtained jointly with Langer to the case of matrix-valued functions. Our main theorems are much more involved than their scalar counterparts. They contain new conditions based on Jordan chains and root functions. The proofs require new techniques based on recent results in the theory of continuous analogs of resultant and Bezout matrices and solutions of certain equations in entire matrix functions. © 2007 Springer Science+Business Media, Inc.
AB - In the mid-fifties, in a seminal paper, M. G. Krein introduced continuous analogs of Szego orthogonal polynomials on the unit circle and established their main properties. In this paper, we generalize these results and subsequent results that he obtained jointly with Langer to the case of matrix-valued functions. Our main theorems are much more involved than their scalar counterparts. They contain new conditions based on Jordan chains and root functions. The proofs require new techniques based on recent results in the theory of continuous analogs of resultant and Bezout matrices and solutions of certain equations in entire matrix functions. © 2007 Springer Science+Business Media, Inc.
U2 - 10.1007/s10688-007-0011-1
DO - 10.1007/s10688-007-0011-1
M3 - Article
SN - 0016-2663
VL - 41
SP - 115
EP - 125
JO - Functional analysis and its Applications
JF - Functional analysis and its Applications
IS - 2
ER -