On a certain functional equation in the algebra of polynomials with complex coefficients

Many analytical problems can be reduced to determining the number of roots of a polynomial in a given disc. In turn, the latter problem admits further reduction to the generalized Rauss-Hurwitz problem of determining the number of roots of a polynomial in a semiplane. However, this procedure require...

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Main Author: E. Muhamadiev
Format: Article
Language:English
Published: Wiley 2006-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/AAA/2006/94509
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author E. Muhamadiev
author_facet E. Muhamadiev
author_sort E. Muhamadiev
collection DOAJ
description Many analytical problems can be reduced to determining the number of roots of a polynomial in a given disc. In turn, the latter problem admits further reduction to the generalized Rauss-Hurwitz problem of determining the number of roots of a polynomial in a semiplane. However, this procedure requires complicated coefficient transformations. In the present paper we suggest a direct method to evaluate the number of roots of a polynomial with complex coefficients in a disc, based on studying a certain equation in the algebra of polynomials. An application for computing the rotation of plane polynomial vector fields is also given.
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spelling doaj-art-c53d52569ea24f9e87a3d87047bf7ee32025-08-20T02:18:48ZengWileyAbstract and Applied Analysis1085-33751687-04092006-01-01200610.1155/AAA/2006/9450994509On a certain functional equation in the algebra of polynomials with complex coefficientsE. Muhamadiev0Department of Information Systems Technologies, Vologda State Technical University, 15 Lenin Street, Vologda 160035, RussiaMany analytical problems can be reduced to determining the number of roots of a polynomial in a given disc. In turn, the latter problem admits further reduction to the generalized Rauss-Hurwitz problem of determining the number of roots of a polynomial in a semiplane. However, this procedure requires complicated coefficient transformations. In the present paper we suggest a direct method to evaluate the number of roots of a polynomial with complex coefficients in a disc, based on studying a certain equation in the algebra of polynomials. An application for computing the rotation of plane polynomial vector fields is also given.http://dx.doi.org/10.1155/AAA/2006/94509
spellingShingle E. Muhamadiev
On a certain functional equation in the algebra of polynomials with complex coefficients
Abstract and Applied Analysis
title On a certain functional equation in the algebra of polynomials with complex coefficients
title_full On a certain functional equation in the algebra of polynomials with complex coefficients
title_fullStr On a certain functional equation in the algebra of polynomials with complex coefficients
title_full_unstemmed On a certain functional equation in the algebra of polynomials with complex coefficients
title_short On a certain functional equation in the algebra of polynomials with complex coefficients
title_sort on a certain functional equation in the algebra of polynomials with complex coefficients
url http://dx.doi.org/10.1155/AAA/2006/94509
work_keys_str_mv AT emuhamadiev onacertainfunctionalequationinthealgebraofpolynomialswithcomplexcoefficients