On the Lorentz degree of a product of polynomials

Rachid Ait-Haddou

doi:10.1016/j.jat.2014.10.001

On the Lorentz degree of a product of polynomials

Rachid Ait-Haddou^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this note, we negatively answer two questions of T. Erdélyi (1991, 2010) on possible lower bounds on the Lorentz degree of product of two polynomials. We show that the correctness of one question for degree two polynomials is a direct consequence of a result of Barnard et al. (1991) on polynomials with nonnegative coefficients.

Original language	English
Pages (from-to)	81-87
Number of pages	7
Journal	Journal of Approximation Theory
Volume	189
DOIs	https://doi.org/10.1016/j.jat.2014.10.001
State	Published - 1 Jan 2015
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.

Keywords

Bernstein bases
Bézier curves
Degree elevation
Lorentz degree
Polynomials with nonnegative coefficients
Pólya degree

ASJC Scopus subject areas

Analysis
Numerical Analysis
General Mathematics
Applied Mathematics

Access to Document

10.1016/j.jat.2014.10.001

Cite this

@article{e9a49cebe4514518a0289ae7a0c1564f,

title = "On the Lorentz degree of a product of polynomials",

abstract = "In this note, we negatively answer two questions of T. Erd{\'e}lyi (1991, 2010) on possible lower bounds on the Lorentz degree of product of two polynomials. We show that the correctness of one question for degree two polynomials is a direct consequence of a result of Barnard et al. (1991) on polynomials with nonnegative coefficients.",

keywords = "Bernstein bases, B{\'e}zier curves, Degree elevation, Lorentz degree, Polynomials with nonnegative coefficients, P{\'o}lya degree",

author = "Rachid Ait-Haddou",

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2015",

month = jan,

day = "1",

doi = "10.1016/j.jat.2014.10.001",

language = "English",

volume = "189",

pages = "81--87",

journal = "Journal of Approximation Theory",

issn = "0021-9045",

}

TY - JOUR

T1 - On the Lorentz degree of a product of polynomials

AU - Ait-Haddou, Rachid

PY - 2015/1/1

Y1 - 2015/1/1

N2 - In this note, we negatively answer two questions of T. Erdélyi (1991, 2010) on possible lower bounds on the Lorentz degree of product of two polynomials. We show that the correctness of one question for degree two polynomials is a direct consequence of a result of Barnard et al. (1991) on polynomials with nonnegative coefficients.

AB - In this note, we negatively answer two questions of T. Erdélyi (1991, 2010) on possible lower bounds on the Lorentz degree of product of two polynomials. We show that the correctness of one question for degree two polynomials is a direct consequence of a result of Barnard et al. (1991) on polynomials with nonnegative coefficients.

KW - Bernstein bases

KW - Bézier curves

KW - Degree elevation

KW - Lorentz degree

KW - Polynomials with nonnegative coefficients

KW - Pólya degree

UR - https://www.scopus.com/pages/publications/84910093832

U2 - 10.1016/j.jat.2014.10.001

DO - 10.1016/j.jat.2014.10.001

M3 - Article

AN - SCOPUS:84910093832

SN - 0021-9045

VL - 189

SP - 81

EP - 87

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

ER -

On the Lorentz degree of a product of polynomials

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this