Complex Polynomials

by T. Sheil-Small

Overview

Complex Polynomials explores the geometric theory of polynomials and rational functions in the plane. Early chapters build the foundations of complex variable theory, melding together ideas from algebra, topology, and analysis. Throughout the book, the author introduces a variety of ideas and constructs theories around them, incorporating much of the classical theory of polynomials as he proceeds. These ideas are used to study a number of unsolved problems. Several solutions to problems are given, including a comprehensive account of the geometric convolution theory.

Product Details

ISBN-13:	9780521400688
Publisher:	Cambridge University Press
Publication date:	11/07/2002
Series:	Cambridge Studies in Advanced Mathematics , #75
Pages:	452
Product dimensions:	6.26(w) x 9.33(h) x 1.10(d)

Table of Contents

Preface; List of notation; 1. The algebra of polynomials; 2. The degree principle and the fundamental theorem of algebra; 3. The Jacobian problem; 4. Analytic and harmonic functions in the unit disc; 5. Circular regions and Grace's theorem; 6. The Ilieff-Sendov conjecture; 7. Self-inversive polynomials; 8. Duality and an extension of Grace's theorem to rational functions; 9. Real polynomials; 10. Level curves; 11. Miscellaneous topics; References; Index.

Editorial Reviews

"...a very welcome addition to the literature dealing with polynomials. ...will be invaluable to researchers and accessible to non-experts as well. I recommend it enthusiastically." Mathematical Reviews

"As both focused study and a joyride across the expanse of modern mathematics, this compilation of results by Sheil-Small would prject polynomial mathematics as a cohesive subject all its own.... Highly recommended." Choice

From the Publisher