Abstract and Applied Analysis

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

E. Muhamadiev

Full-text: Open access

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


Export citation

References

  • N. G. Chebotarev and N. N. Meyman, Rauss-Hurwitz stability problem for polynomials and entire functions, Trudy Matematicheskogo Instituta Imeni V. A. Steklova 26 (1949).
  • B. P. Demidovič, Lectures on the Mathematical Theory of Stability, Izdat. “Nauka”, Moscow, 1967.
  • F. R. Gantmaher, Matrix Theory, Nauka, Moscow, 1967.
  • M. A. Krasnosel'sky, A. I. Perov, A. I. Povolotsky, and P. P. Zabreiko, Plane Vector Fields, Fizmatgiz, Moscow, 1961.
  • V. V. Prasolov, Polynomials, MCNMO, Moscow, 2003.