Analytic Continuation of Cauchy and Exponential Transforms

  • Björn Gustafsson
  • Mihai Putinar
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 9)


We review some recent results concerning analytic continuation properties of the Cauchy transform of a domain in the complex plane, of a corresponding exponential transform and of the resolvent of a hyponormal operator associated with the domain.

The main result states the equivalence between the mentioned analytic continuations. As a corollary we obtain apriori regularity of boundaries admitting analytic continuation of the Cauchy transform.


Unit Disc Analytic Continuation Algebraic Curve Extremal Solution Quadrature Domain 
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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Björn Gustafsson
    • 1
  • Mihai Putinar
    • 2
  1. 1.Mathematics DepartmentRoyal Institute of TechnologyStockholmSweden
  2. 2.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA

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