Abstract and Applied Analysis
Volume 2006 (2006), Article ID 94509, 15 pages
doi: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.