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Stieltjes Property of Quasi-Stable Matrix Polynomials

Author

Listed:
  • Xuzhou Zhan

    (Department of Mathematics, Beijing Normal University at Zhuhai, Zhuhai 519087, China)

  • Bohui Ban

    (School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China)

  • Yongjian Hu

    (Department of Mathematics, Beijing Normal University at Zhuhai, Zhuhai 519087, China
    School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China)

Abstract

In this paper, basing on the theory of matricial Hamburger moment problems, we establish the intrinsic connections between the quasi-stability of a monic or comonic matrix polynomial and the Stieltjes property of a rational matrix-valued function built from the even–odd split of the original matrix polynomial. As applications of these connections, we obtain some new criteria for quasi-stable matrix polynomials and Hurwitz stable matrix polynomials, respectively.

Suggested Citation

  • Xuzhou Zhan & Bohui Ban & Yongjian Hu, 2022. "Stieltjes Property of Quasi-Stable Matrix Polynomials," Mathematics, MDPI, vol. 10(23), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4440-:d:983290
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