Abstract
It is shown that the class of 2 × 2 J-inner matrix functions of the form where A k J ≥ 0 for k = 1,…, n, have an essentially unique multiplicative decomposition. This is a very special case of a deep theorem of de Branges. However, the method of proof is new and elementary. [Abstract added by editors.]
Translated from: Analiz v beskonečnomernyh prostranstvah i teorija operatorov. (“Naukova Dumka” publishing house, Kiev, 1983, V.A.Marchenko — ed. ), 101–117.
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References
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Mikhailova, I.V. (1997). Weyl matrix circles as a tool for uniqueness in the theory of multiplicative representation of J-inner matrix functions. In: Dym, H., Katsnelson, V., Fritzsche, B., Kirstein, B. (eds) Topics in Interpolation Theory. Operator Theory Advances and Applications, vol 95. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8944-5_19
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