Complex Polynomials

ISBN-13: 9780521400688 / Angielski / Twarda / 2002 / 452 str.

T. Sheil-Small; B. Bollobas; W. Fulton

Opis

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.

Recenzje

"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

Spis treści

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.