The Inverse Problem for Krein Orthogonal Matrix Functions

I. Ts. Gokhberg ; M. A. Kaashoek ; L. E. Lerer

Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 2, pp. 44-57.

Résumé

In the mid-fifties, in a seminal paper, M. G. Krein introduced continuous analogs of Szegő 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.

Détail

Keywords: Krein orthogonal function, continuous analog of orthogonal polynomials, entire matrix function equation, root function, inverse problem.
Mots-clés : Jordan chain

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