## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2006, Special Issue (2006), Article ID 94509, 15 pages.

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

#### 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.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2006, Special Issue (2006), Article ID 94509, 15 pages.

**Dates**

First available in Project Euclid: 19 March 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1174321757

**Digital Object Identifier**

doi:10.1155/AAA/2006/94509

**Mathematical Reviews number (MathSciNet)**

MR2251797

**Zentralblatt MATH identifier**

1143.30007

#### Citation

Muhamadiev, E. On a certain functional equation in the algebra of polynomials with complex coefficients. Abstr. Appl. Anal. 2006, Special Issue (2006), Article ID 94509, 15 pages. doi:10.1155/AAA/2006/94509. https://projecteuclid.org/euclid.aaa/1174321757