Abstract
The generalized Schur transform as defined in [13] (see also [2][6]) is applied to the class A° of all complex-valued functions, which are holomorphic at z = O. Each such function has a coisometric and a unitary realization in some Krein space. We study the effect of this generalized Schur transform to the unitary realization; in [2], [3] we studied similar questions for the coisometric realizations. The main difference with [2], [3] is that a certain one-sidedness is replaced by a two-sidedness, comparable to the difference between the unilateral shift on one-sided sequences and the shift on two-sided sequences. We follow a direct approach in line with [2, 3, 6].
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Alpay, D., Azizov, T.Y., Dijksma, A., Langer, H., Wanjala, G. (2004). The Schur Algorithm for Generalized Schur Functions IV: Unitary Realizations. In: Ball, J.A., Helton, J.W., Klaus, M., Rodman, L. (eds) Current Trends in Operator Theory and its Applications. Operator Theory: Advances and Applications, vol 149. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7881-4_2
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DOI: https://doi.org/10.1007/978-3-0348-7881-4_2
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