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A Potapov-Type Approach to a Truncated Matricial Stieltjes-Type Power Moment Problem

In: Advancements in Complex Analysis

Author

Listed:
  • Bernd Fritzsche

    (University of Leipzig, Department of Mathematics)

  • Bernd Kirstein

    (University of Leipzig, Department of Mathematics)

  • Conrad Mädler

    (University of Leipzig)

  • Tatsiana Makarevich

    (Fakultät für Mathematik und Informatik, Universität Leipzig)

Abstract

The paper gives a parametrization of the solution set of a matricial Stieltjes-type truncated power moment problem in the non-degenerate and degenerate cases. The key role plays the solution of the corresponding system of Potapov’s fundamental matrix inequalities. The original matricial moment problem will be reformulated in a system of interpolation problems for distinguished classes of holomorphic q × q matrix-valued functions. A key instrument of our strategy is to use an appropriate synthesis of techniques from the theory of meromorphic matrix-valued functions with elements from the J-theory due to V. P. Potapov.

Suggested Citation

  • Bernd Fritzsche & Bernd Kirstein & Conrad Mädler & Tatsiana Makarevich, 2020. "A Potapov-Type Approach to a Truncated Matricial Stieltjes-Type Power Moment Problem," Springer Books, in: Daniel Breaz & Michael Th. Rassias (ed.), Advancements in Complex Analysis, pages 193-297, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-40120-7_6
    DOI: 10.1007/978-3-030-40120-7_6
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