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Polynomial interpolation problem for skew polynomials

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2007
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Authors
Erić, Aleksandra
Article (Published version)
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Abstract
Let R = K[x;δ] be a skew polynomial ring over a division ring K. We introduce the notion of derivatives of skew polynomial at scalars. An analogous definition of derivatives of commutative polynomials from K[x] as a function of K[x] → K[x] is not possible in a non-commutative case. This is the reason why we have to define the derivative of a skew polynomial at a scalar. Our definition is based on properties of skew polynomial rings, and it makes possible some useful theorems about them. The main result of this paper is a generalization of polynomial interpolation problem for skew polynomials. We present conditions under which there exists a unique polynomial of a degree less then n which takes prescribed values at given points xi Є K (1 ≤ n). We also discuss some kind of Silvester-Lagrange skew polynomial.
Keywords:
interpolation / skew polynomials
Source:
Applicable Analysis and Discrete Mathematics, 2007, 1, 2, 403-414
Publisher:
  • Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd

DOI: 10.2298/AADM0702403E

ISSN: 1452-8630

WoS: 000207680700009

Scopus: 2-s2.0-78650939388
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URI
https://grafar.grf.bg.ac.rs/handle/123456789/161
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  • Radovi istraživača / Researcher's publications
  • Катедра за математику, физику и нацртну геометрију
Institution/Community
GraFar
TY  - JOUR
AU  - Erić, Aleksandra
PY  - 2007
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/161
AB  - Let R = K[x;δ] be a skew polynomial ring over a division ring K. We introduce the notion of derivatives of skew polynomial at scalars. An analogous definition of derivatives of commutative polynomials from K[x] as a function of K[x] → K[x] is not possible in a non-commutative case. This is the reason why we have to define the derivative of a skew polynomial at a scalar. Our definition is based on properties of skew polynomial rings, and it makes possible some useful theorems about them. The main result of this paper is a generalization of polynomial interpolation problem for skew polynomials. We present conditions under which there exists a unique polynomial of a degree less then n which takes prescribed values at given points xi Є K (1 ≤ n). We also discuss some kind of Silvester-Lagrange skew polynomial.
PB  - Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd
T2  - Applicable Analysis and Discrete Mathematics
T1  - Polynomial interpolation problem for skew polynomials
EP  - 414
IS  - 2
SP  - 403
VL  - 1
DO  - 10.2298/AADM0702403E
ER  - 
@article{
author = "Erić, Aleksandra",
year = "2007",
abstract = "Let R = K[x;δ] be a skew polynomial ring over a division ring K. We introduce the notion of derivatives of skew polynomial at scalars. An analogous definition of derivatives of commutative polynomials from K[x] as a function of K[x] → K[x] is not possible in a non-commutative case. This is the reason why we have to define the derivative of a skew polynomial at a scalar. Our definition is based on properties of skew polynomial rings, and it makes possible some useful theorems about them. The main result of this paper is a generalization of polynomial interpolation problem for skew polynomials. We present conditions under which there exists a unique polynomial of a degree less then n which takes prescribed values at given points xi Є K (1 ≤ n). We also discuss some kind of Silvester-Lagrange skew polynomial.",
publisher = "Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd",
journal = "Applicable Analysis and Discrete Mathematics",
title = "Polynomial interpolation problem for skew polynomials",
pages = "414-403",
number = "2",
volume = "1",
doi = "10.2298/AADM0702403E"
}
Erić, A.. (2007). Polynomial interpolation problem for skew polynomials. in Applicable Analysis and Discrete Mathematics
Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd., 1(2), 403-414.
https://doi.org/10.2298/AADM0702403E
Erić A. Polynomial interpolation problem for skew polynomials. in Applicable Analysis and Discrete Mathematics. 2007;1(2):403-414.
doi:10.2298/AADM0702403E .
Erić, Aleksandra, "Polynomial interpolation problem for skew polynomials" in Applicable Analysis and Discrete Mathematics, 1, no. 2 (2007):403-414,
https://doi.org/10.2298/AADM0702403E . .

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