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The cone of nonnegative polynomials with nonnegative coefficients and linear operators preserving this cone

✍ Scribed by Katkova, Olga ;Vishnyakova, Anna

Book ID
121551244
Publisher
Walter de Gruyter GmbH
Year
2014
Tongue
English
Weight
919 KB
Volume
12
Category
Article
ISSN
2391-5455

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✦ Synopsis

Abstract

Let be the cone of real univariate polynomials of degree ≀ 2n which are nonnegative on the real axis and have nonnegative coefficients. We describe the extremal rays of this convex cone and the class of linear operators, acting diagonally in the standard monomial basis, preserving this cone.

πŸ“œ SIMILAR VOLUMES

Local spectral radii and Collatz-Wieland
Local spectral radii and Collatz-Wielandt numbers of monic operator polynomials with nonnegative coefficients
✍ K.-H. FΓΆrster; B. Nagy πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 666 KB

Operator polynomials L(A)= htI-A I 1A l\_ 1 ..... hA 1 -A o are considered, where A0,..., A t\_l are nonnegative operators in a Banach space ~ with normal cone ~+. For x G ~-o~+ we define the local spectral radius rL(x) and the lower and upper Collatz-Wielandt numbers rL(x) and rL(x), respectively,