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Discrepancy of Signed Measures and Polynomial Approximation / Edition 1
     

Discrepancy of Signed Measures and Polynomial Approximation / Edition 1

by Vladimir V. Andrievskii, Hans-Peter Blatt
 

ISBN-10: 0387986529

ISBN-13: 9780387986524

Pub. Date: 12/14/2001

Publisher: Springer New York

The book is an authoritative and up-to-date introduction to the field of analysis and potential theory dealing with the distribution zeros of classical systems of polynomials such as orthogonal polynomials, Chebyshev, Fekete and Bieberbach polynomials, best or near-best approximating polynomials on compact sets and on the real line. The main feature of the book is the

Overview

The book is an authoritative and up-to-date introduction to the field of analysis and potential theory dealing with the distribution zeros of classical systems of polynomials such as orthogonal polynomials, Chebyshev, Fekete and Bieberbach polynomials, best or near-best approximating polynomials on compact sets and on the real line. The main feature of the book is the combination of potential theory with conformal invariants, such as module of a family of curves and harmonic measure, to derive discrepancy estimates for signed measures if bounds for their logarithmic potentials or energy integrals are known a priori.

Product Details

ISBN-13:
9780387986524
Publisher:
Springer New York
Publication date:
12/14/2001
Series:
Springer Monographs in Mathematics Series
Edition description:
2002
Pages:
438
Product dimensions:
1.06(w) x 6.14(h) x 9.21(d)

Table of Contents

* Preface
• Auxiliary Facts
• Zero Distribution of Polynomials
• Discrepancy Theorems via Two-Sided Bounds for Potentials
• Discrepancy Thoerems via One-Sided Bounds for Potentials
• Discrepancy Theorems via Energy Integrals
• Applications of Jentzsch-Szegö and Erdös-Turán Type Theorems
• Applications of Discrepancy Theorems
• Special Topics
• Appendix A: Conformally INvariant Characteristics of Curve Families
• Appendix B: Basics in the Theory of Quasiconformal Mappings
• Appendix C: Constructive Theory of Functions of a Complex Variable
• Appendix D: Miscellaneous Topics
• Bibliography
• Glossary of Notation
• Index *

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