Abstract
The constructions described in Sec. 1 are applied to the investigation of the abstract interpolation problem. The general solution of the problem is the characteristic function of an operator colligation, obtained by the closure of fixed colligation by means of an arbitrary colligation with definite exterior spaces. The complete integral representation of a nonnegative quadratic form is obtained by applying Parseval's equality, considered in Sec. 1.
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Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 50, pp. 98–103, 1988.
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Kheifets, A.Y. Parseval's equality in the abstract interpolation problem and the coupling of open systems. II. J Math Sci 49, 1307–1310 (1990). https://doi.org/10.1007/BF02209179
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DOI: https://doi.org/10.1007/BF02209179