Abstract
For a class of pairs of entire matrix functions the null space of the natural analogue of the classical resultant matrix is described in terms of the common Jordan chains of the defining entire matrix functions. The main theorem is applied to two inverse problems. The first concerns convolution integral operators on a finite interval with matrix valued kernel functions and complements earlier results of [6]. The second is the inverse problem for matrix-valued continuous analogues of Szegő orthogonal polynomials.
The research of the third author was partially supported by a visitor fellowship of the Netherlands Organization for Scientific Research (NWO) and the Glasberg-Klein Research Fund at the Technion.
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Gohberg, I., Kaashoek, M.A., Lerer, L. (2006). The Continuous Analogue of the Resultant and Related Convolution Operators. In: Dritschel, M.A. (eds) The Extended Field of Operator Theory. Operator Theory: Advances and Applications, vol 171. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7980-3_6
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