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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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA/2006/94509 |
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| _version_ | 1850178132244430848 |
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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. |
| format | Article |
| id | doaj-art-c53d52569ea24f9e87a3d87047bf7ee3 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| 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 |