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

E. Muhamadiev

Abstract and Applied Analysis, 2006, vol. 2006, 1-15

Abstract:

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.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:094509

DOI: 10.1155/AAA/2006/94509

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