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Abstract and Applied Analysis
Volume 2006 (2006), Article ID 94509, 15 pages
http://dx.doi.org/10.1155/AAA/2006/94509

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

Department of Information Systems Technologies, Vologda State Technical University, 15 Lenin Street, Vologda 160035, Russia

Received 26 June 2005; Accepted 1 July 2005

Copyright © 2006 E. Muhamadiev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.