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

Olga Katkova; Anna Vishnyakova

Open Mathematics (2014)

- Volume: 12, Issue: 5, page 752-760
- ISSN: 2391-5455

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topOlga Katkova, and Anna Vishnyakova. "The cone of nonnegative polynomials with nonnegative coefficients and linear operators preserving this cone." Open Mathematics 12.5 (2014): 752-760. <http://eudml.org/doc/269561>.

@article{OlgaKatkova2014,

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.},

author = {Olga Katkova, Anna Vishnyakova},

journal = {Open Mathematics},

keywords = {Positive polynomials; Nonnegative polynomials; Nonnegative polynomials with nonnegative coefficients; Extremal rays of convex cone; Linear positivity preservers; positive polynomial; extremal rays of convex cone; linear operator},

language = {eng},

number = {5},

pages = {752-760},

title = {The cone of nonnegative polynomials with nonnegative coefficients and linear operators preserving this cone},

url = {http://eudml.org/doc/269561},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Olga Katkova

AU - Anna Vishnyakova

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

JO - Open Mathematics

PY - 2014

VL - 12

IS - 5

SP - 752

EP - 760

AB - 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.

LA - eng

KW - Positive polynomials; Nonnegative polynomials; Nonnegative polynomials with nonnegative coefficients; Extremal rays of convex cone; Linear positivity preservers; positive polynomial; extremal rays of convex cone; linear operator

UR - http://eudml.org/doc/269561

ER -

## References

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- [5] Katkova O.M., Vishnyakova A.M., Linear operators preserving the set of positive (nonnegative) polynomials, In: Positive Systems, Valencia, September 2–4, 2009, Lecture Notes in Control and Inform. Sci., 389, Springer, Berlin, 2009, 83–90 Zbl1182.93061
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