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The natural attempt to analyze the general principles inherent in various classes of functions (positive, Nevanlinna, contractive, etc.), as well as the search for a uniform method for their research, lead to elementary concepts of J-theory. The study of similar matrix-valued classes of functions, due to the non-commutativity of the matrix algebra, encounters significant, fundamental difficulties, which served as the source for creating a new research apparatus, J-theory.

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Elements of V.P. Potapov’s J-Theory and the Factorization Problem of J-Contractive Matrix Functions

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  • 发表日期：

    2025年

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  • Vladimir A. Zolotarev

摘要

The natural attempt to analyze the general principles inherent in various classes of functions (positive, Nevanlinna, contractive, etc.), as well as the search for a uniform method for their research, lead to elementary concepts of J-theory. The study of similar matrix-valued classes of functions, due to the non-commutativity of the matrix algebra, encounters significant, fundamental difficulties, which served as the source for creating a new research apparatus, J-theory.