Analytic continuation of Cauchy and exponential transforms (Q2749816)

This is a review of the authors' recent results devoted to analytic continuation properties of the three following objects: the Cauchy transform of a domain in the complex plane, the corresponding exponential transform, and the resolvent of a hyponormal operator associated with the domain. The main result is that the three above objects admit analytic continuations from outside the domain across its boundary under the same conditions. As an application, the a priori regularity of boundaries admitting analytic continuation of the Cauchy transform is given.NEWLINENEWLINEFor the entire collection see [Zbl 0963.00016].