Abstract
A generalized Schur function which is holomorphic at z = 0 can be written as the characteristic function of a closely connected unitary colligation with a Pontryagin state space. We describe the closely connected unitary colligation of a solution s(z) of the basic interpolation problem for generalized Schur functions (studied in [3]) in terms of the interpolation data and the canonical unitary colligation of the parameter function s1(z) appearing in the formula for s(z). In particular, we consider the case where the interpolation data and the Taylor coefficients of s1(z) at z = 0 are real. We also show that the canonical unitary colligation of s1(z) can be recovered from that of s(z).
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© 2005 Birkhäuser Verlag Basel/Switzerland
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Wanjala, G. (2005). Closely Connected Unitary Realizations of the Solutions to the Basic Interpolation Problem for Generalized Schur Functions. In: Gohberg, I., et al. Recent Advances in Operator Theory and its Applications. Operator Theory: Advances and Applications, vol 160. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7398-9_23
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DOI: https://doi.org/10.1007/3-7643-7398-9_23
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