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: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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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| ISSN: | 1085-3375 1687-0409 |