The Logarithmic Integral Converges

  • Victor Havin
  • Burglind Jöricke
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete / A Series of Modern Surveys in Mathematics book series (MATHE3, volume 28)


Divergence of a logarithmic integral is the principal sufficient condition of many forms of the UP. But in fact it coincides with the necessary condition. The logarithmic integral determines a border-line separating two realms, the one undividedly governed by the UP (and described in Chapter 2) and the other where the resistance to the UP is possible and non-zero pairs (f, f̂) are allowed whose elements are small simultaneously. This chapter is devoted to methods of construction (or at least to the existence proofs) of such pairs.


Characteristic Function Entire Function Tauberian Theorem Homogeneous Mass Logarithmic Potential 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Victor Havin
    • 1
  • Burglind Jöricke
    • 2
  1. 1.Department of MathematicsSt. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Max-Planck-Gesellschaft zur Förderung der WissenschaftenBerlinGermany

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