Analytic Continuation of Cauchy and Exponential Transforms
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.
KeywordsUnit Disc Analytic Continuation Algebraic Curve Extremal Solution Quadrature Domain
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