Abstract
An improvement and generalization of V.P. Potapov’s theory of the J-modulus is established. The results, in the special case J = I, are applied to obtain the representation by a multiplicative integral of an operator-valued outer function f from the values at some interior point of the disc of the moduli of certain divisors of f, or from the moduli of the boundary values of f. [Abstract added by editors.]
Translated from: Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. No.41 (1984), 135–143. MR 85k:47063
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References
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Potapov, V.P., A theorem on the modulus, I. Fundamental concepts. The modulus. Teor. Functsiĭ Funksional Anal. i Prilozh. 38 (1982), 91–101 (Russian). English transl.: Amer. Math. Soc. Transl. (2) 138 (1988), 55–66.
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Ginzburg, Y.P. (1997). On recovering a multiplicative integral from its modulus. 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_9
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DOI: https://doi.org/10.1007/978-3-0348-8944-5_9
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