Journal d’Analyse Mathématique

, Volume 45, Issue 1, pp 1–36 | Cite as

Grunsky inequalities and Fredholm spectrum in general domains

  • Jacob Burbea
Article
Received:

Abstract

We discuss the Fredholm spectrum for general domains and study its applications to conformal and quasi-conformal mappings. In particular, we establish an improvement of the Grunsky inequalities which is valid for general domains. This improvement constitutes an extension of a recent result of Schiffer concerning the sharpening of Grunsky inequalities for the unit disk by a factor smaller than 1, and which is the reciprocal of the least Fredholm eigenvalue of the smooth simply-connected image domain.

Keywords

Unit Disk General Domain Bergman Kernel Circular Domain Schwarzian Derivative 
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Copyright information

© The Weizmann Science Press of Israel 1985

Authors and Affiliations

  • Jacob Burbea
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of PittsburghPittsburghUSA
  2. 2.Mathematics Science DepartmentIBM T. J. Watson Research CenterYorktown HeightsUSA

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