Stieltjes Property of Quasi-Stable Matrix Polynomials

Xuzhou Zhan, Bohui Ban and Yongjian Hu ()
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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

Mathematics, 2022, vol. 10, issue 23, 1-19

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.

Keywords: matrix polynomial; quasi-stability; Hurwitz stability; Hamburger moment problem; Nevanlinna function; Stieltjes function; stability index; degeneracy index (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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