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Table of contents:
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-Sendoff 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.
This book studies the geometric theory of polynomials and rational functions in the plane. The theory is carefully constructed bearing in mind the needs of graduate students. Several unsolved problems are presented as well as the full solutions to some well known conjectures.
Geometric theory of polynomials and rational functions for graduate students and researchers.
- Verlag: Cambridge University Press
- Seitenzahl: 452
- Erscheinungstermin: 30. Oktober 2007
- Abmessung: 235mm x 157mm x 30mm
- Gewicht: 882g
- ISBN-13: 9780521400688
- ISBN-10: 0521400686
- Artikelnr.: 22308892