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Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations by Harry Dym, Damir Z. Arov

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9Bitangential Krein extension problems

In this chapter we shall discuss bitangential generalizations of matrix versions of two classical extension problems that were introduced by M.G. Krein: the helical extension problem and the accelerant extension problem, and some analogs of these problems related to the Schur class Sp×q (instead of the Carathéodory class Cp×p). These extension problems will be identified with the generalized interpolation problems GCIP(b3, b4; c°) and GSIP(b1, b2; s°) with appropriately chosen mvf’s c° ∈ Cp×p, s° ∈ Sp×q and entire inner mvf’s b1,…,b4. We shall make use of the fact that if image, b(0) = Ip and τb = a, then, by ...

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