Abstract
In this paper, especially in Sections 1–3, we give an account of the author’s results concerning J-inner matrix-functions and related continuation problems stated in [1] and whose proofs can be found in [2]. They are supplemented, in Section 4, 5, with some results about the solutions of the continuation problem with maximal jump of the spectral function, which are obtained using a generalization of Carathéodory Theorem on holomorphic contractive scalar functions in the case of matrix-valued functions. For the significance of J-inner matrix-functions in various problems of Mathematical Analysis and their applications, see [3–6], [25, 26].
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Arov, D.Z. (1990). Regular J-Inner Matrix-Functions and Related Continuation Problems. In: Helson, H., Sz.-Nagy, B., Vasilescu, FH., Arsene, G. (eds) Linear Operators in Function Spaces. Operator Theory: Advances and Applications, vol 43. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7250-8_3
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