Advertisement

Discrepancy of Signed Measures and Polynomial Approximation

  • Vladimir V. Andrievskii
  • Hans-Peter Blatt

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Vladimir V. Andrievskii, Hans-Peter Blatt
    Pages 1-48
  3. Vladimir V. Andrievskii, Hans-Peter Blatt
    Pages 49-93
  4. Vladimir V. Andrievskii, Hans-Peter Blatt
    Pages 95-128
  5. Vladimir V. Andrievskii, Hans-Peter Blatt
    Pages 129-172
  6. Vladimir V. Andrievskii, Hans-Peter Blatt
    Pages 173-186
  7. Vladimir V. Andrievskii, Hans-Peter Blatt
    Pages 187-224
  8. Vladimir V. Andrievskii, Hans-Peter Blatt
    Pages 225-319
  9. Vladimir V. Andrievskii, Hans-Peter Blatt
    Pages 321-340
  10. Back Matter
    Pages 341-438

About this book

Introduction

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. Classical results of Jentzsch and Szegö for the zero distribution of partial sums of power series can be recovered and sharpened by new discrepany estimates, as well as distribution results of Erdös and Turn for zeros of polynomials bounded on compact sets in the complex plane.
Vladimir V. Andrievskii is Assistant Professor of Mathematics at Kent State University. Hans-Peter Blatt is Full Professor of Mathematics at Katholische Universität Eichstätt.

Keywords

Approximation Theory Complex Analysis Constructive Analysis Geometric Function Theory Invariant Polynomials Potential Theory Variable calculus function theorem

Authors and affiliations

  • Vladimir V. Andrievskii
    • 1
  • Hans-Peter Blatt
    • 2
  1. 1.Department of Mathematics and Computer ScienceKent State UniversityKentUSA
  2. 2.Mathematisch-Geographische FakultätKatholische Universität EichstättEichstättGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-4999-1
  • Copyright Information Springer-Verlag New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3146-7
  • Online ISBN 978-1-4757-4999-1
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site