Degree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9 (Annals of Mathematics Studies (9))

The description for this book, Degree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9, will be forthcoming. PREFACE CONTENTS Chapter I. PRELIMINARIES §1. Statement of the Problems; Notation §2. Lipschitz Conditions and Derivatives §3. Exercises §4. Discussion PART I. PROBLEM α Chapter II. POLYNOMIAL INEQUALITIES §1. A Polynomial and its Derivarives §2. A Polynomial and its Integral §3. The Lagrange-Hermite Interpolation Formula §4. Geometric Properties of Equipotential Curves §5. Equally Distributed Points §6. Exercises §7. Open Problems Chapter III. TCHEBYCHEFF APPROXIMATION §1. Jackson's Theorem on Trigonometric Approximation §2. Direct Theorems §3. The Faber Polynomials §4. Indirect Theorems §5. The Derivative and Integral of a Function §6. Best Approximation §7. Exercises §8. Open Problems Chapter IV. APPROXIMATION MEASURED BY A LINE INTEGRAL §1. Direct Theorems §2. Indirect Theorems §3. Orthogonal Polynomials §4. Polynomials of Best Approximation §5. Generality of the Weight Function §6. Exercises §7. Discussion PART II. PROBLEM β Chapter V. PRELIMINARIES §1. An Interpolation Formula and Inequalities §2. An Extended Classification §3. A Polynomial and its Integral §4. Exercises §5. Open Problems Chapter VI. TCHEBYCHEFF APPROXIMATION §1. Direct Theorems §2. Operations with Approximating Sequences §3. Indirect Theorems §4. Counter Examples §5. Functions with Isolated Singularities §6. Polynomials of Best Approximation §7. Exercises §6. Discussion Chapter VII. APPROXIMATION MEASURED BY A LINE INTEGRAL §1. Direct Theorems §2. Indirect Theorems §3. Orthogonal Polynomials §4. Polynomials of Best Approximation §5. Generality of the Weight Function §6. Exercises §7. Discussion Chapter VIII. SPECIAL CONFIGURATIONS §1. Approximation on |z| = 1 by Polynomials in z and 1/z §2. Approximation on -1 ≦ z ≦ 1 §3. Trigonometric Approximation §4. Direct Methods on Problem α and Problem β §5. Exercises §6. Discussion Bibliography A classic treatment of degree of approximation by polynomials in the complex domain from the acclaimed Annals of Mathematics Studies seriesPrinceton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century.To mark the continued success of the series, all books are available in paperback and as ebooks. The book description for the forthcoming "Degree of Approximation by Polynomials in the Complex Domain. (AM-9)" is not yet available.