Opuscula Math. 25, no. 2 (2005), 189-194

Opuscula Mathematica

Convex compact family of polynomials and its stability

Michał Góra

Abstract. Let \(P\) be a set of real polynomials of degree \(n\). Set \(P\) can be identified with some subset \(P\) of \(\mathbb{R}^n\) consists of vectors of coefficients of \(P\). If \(P\) is a polytope, then to ascertain whether the entire family of polynomials \(P\) is stable or not, it suffices to examine the stability of the one-dimensional boundary sets of \(P\). In present paper, we extend this result to convex compact polynomial families. Examples are presented to illustrate the results.

Keywords: stability, convex set of polynomials, regular set.

Mathematics Subject Classification: 26C10, 30C15, 52A20, 65L07.

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  • Michał Góra
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland
  • Received: 2004-10-22.
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Michał Góra, Convex compact family of polynomials and its stability, Opuscula Math. 25, no. 2 (2005), 189-194

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