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Hilbert's boundary-value problem (with coefficients from the Wiener ring) for matrix-valued functions analytic in the unit disk

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Abstract

Hilbert's boundary-value problem is stated and solved for matrix-valued functions, analytic in the unit disk, under the condition that the coefficients and the free term belong to the Wiener ring (ℜ(n×n)). Left standard factorization of the coefficientU(t) leads to the determination of the number of linearly independent solutions of the homogeneous problem and the number and type of conditions under which the inhomogeneous problem is solvable.

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Literature cited

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Authors and Affiliations

  1. P. G. Tychin Umansk State Pedagogical Institute, USSR

    A. L. Lukov

Authors
  1. A. L. Lukov
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Translated from Matematicheskie Zametki, Vol. 10, No. 3, pp. 279–286, September, 1971.

I wish to express my gratitude to A. V. Batyrev for help in writing this paper.

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Lukov, A.L. Hilbert's boundary-value problem (with coefficients from the Wiener ring) for matrix-valued functions analytic in the unit disk. Mathematical Notes of the Academy of Sciences of the USSR 10, 591–596 (1971). https://doi.org/10.1007/BF01464718

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  • DOI: https://doi.org/10.1007/BF01464718

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