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arXiv · 0911.5133

On an Interpolation Problem for J-Potapov Functions

Bernd Fritzsche·Bernd Kirstein·Uwe Raabe
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Abstract

Let, J, be an m-by-m-signature matrix and let D be the open unit disk in the complex plane. Denote by P{J,0}(D) the class of all meromorphic m-by-m-matrix-valued functions, f, in D which are holomorphic at 0 and take J-contractive values at all points of D at which f is holomorphic. The central theme of this paper is the study of the following interpolation problem: Let n be a nonnegative integer, and let A_0, A_1, ..., A_n be a sequence of complex m-by-m-matrices. Describe the set of all matrix-valued functions, f, belonging to the class P{J,0}(D), such that the first n+1 Taylor coefficients of f coincide with A_0, A_1, ..., A_n. In particular, we characterize the case that this set is non-empty. In this paper, we will solve this problem in the most general case. Moreover, in the non-degenerate case we will give a description of the corresponding Weyl matrix balls. Furthermore, we will investigate the limit behaviour of the Weyl matrix balls associated with the functions belonging to some particular subclass of P{J,0}(D).

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Bernd Fritzsche, Bernd Kirstein, Uwe Raabe. 2009-11-26. On an Interpolation Problem for J-Potapov Functions. https://arxiv.org/abs/0911.5133

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