The twofold Ellis-Gohberg inverse problem for rational matrix functions on the real line

Abstract

From the mid-1980s R.L. Ellis, I. Gohberg and D.C. Lay wrote several papers on systems of orthogonal matrix polynomials and matrix functions, culminating in the monograph [3] by Ellis and Gohberg, where additional background and further references can be found. Inverse problems related to these orthogonal systems were first considered in [2] for scalar-valued Wiener functions on the circle, both for unilateral systems (onefold problem) and bilateral systems (twofold problem). In later work extensions of the onefold inverse problem on the circle were considered for square matrix-valued polynomials in [5] and for square matrix-valued Wiener functions in [4]. Nonsquare versions were only recently dealt with in [12] and [13] for the onefold problems on the circle and real line, respectively, while nonsquare twofold problems on the circle and real line were solved in [9] and [10], respectively. In this paper we further develop the solution to the twofold inverse problem on the...