Advertisement

Discrepancy Theorems via Two-Sided Bounds for Potentials

  • Vladimir V. Andrievskii
  • Hans-Peter Blatt
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

In potential theory it is well known that a mass distribution σ is uniquely determined by its potential U σ . In this chapter we shall consider different ways of making this fact more precise for signed measures σ = σ +σ that are supported on curves or arcs L.

Keywords

Conformal Mapping Signed Measure Jordan Curve Positive Part Discrepancy Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Historical Comments

  1. [7]
    F. Amoroso, M. Mignotte (1996): On the distribution of the roots of polynomials. Ann. Inst. Fourier (Grenoble), 46: 1275–1291.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [19]
    V.V. Andrievskii, H.-P. Blatt (1997): A discrepancy theorem on quasiconformal curves. Constr. Approx., 13: 363–379.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [21]
    V.V. Andrievskii, H.-P. Blatt, H.N. Mhaskar (2001): A local discrepancy theorem. Indag. Math., N.S., 12 (1): 23–39.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [28]
    H.-P. Blatt (1992): On the distribution of simple zeros of polynomials. J. Approx. Theory, 69: 250–268.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [34]
    H.-P. Blatt, H.N. Mhaskar (1993): A general discrepancy theorem. Ark. Mat., 31: 219–246.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [177]
    V. Totik (1993): Distribution of simple zeros of polynomials. Acta Math., 170: 1–28.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2002

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

Personalised recommendations