Complex polynomials /
Sheil-Small, T. 1937-
Complex polynomials / T. Sheil-Small. - Cambridge ; New York : Cambridge University Press, 2002. - 1 online resource (xix, 428 pages). - Cambridge studies in advanced mathematics ; 75 . - Cambridge studies in advanced mathematics ; 75. .
Includes bibliographical references (pages 416-419) and index.
Cover; Half-title; Series-title; Title; Copyright; Contents; Preface; Notations; 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.
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.
0511065396 9780511065392 0511067526 9780511067525
Polynomials.
Functions of complex variables.
Polynômes.
Fonctions d'une variable complexe.
MATHEMATICS--Algebra--Elementary.
Functions of complex variables.
Polynomials.
Electronic books.
Electronic books.
QA161.P59 / S45 2002eb
512.9/42
Complex polynomials / T. Sheil-Small. - Cambridge ; New York : Cambridge University Press, 2002. - 1 online resource (xix, 428 pages). - Cambridge studies in advanced mathematics ; 75 . - Cambridge studies in advanced mathematics ; 75. .
Includes bibliographical references (pages 416-419) and index.
Cover; Half-title; Series-title; Title; Copyright; Contents; Preface; Notations; 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.
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.
0511065396 9780511065392 0511067526 9780511067525
Polynomials.
Functions of complex variables.
Polynômes.
Fonctions d'une variable complexe.
MATHEMATICS--Algebra--Elementary.
Functions of complex variables.
Polynomials.
Electronic books.
Electronic books.
QA161.P59 / S45 2002eb
512.9/42