Analytic capacity

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Abstract

© Springer International Publishing Switzerland 2014. In this chapter we will introduce the notion of analytic capacity and we will study some of its basic properties, its connection with the Painlevé problem, and its relationship with Hausdorff measures. We will also review some results on the Cauchy transform and Vitushkin’s localization operator that are useful for the study of analytic capacity.
Original languageEnglish
Title of host publicationProgress in Mathematics
Pages15-43
Number of pages28
Volume307
ISBN (Electronic)2296-505X
DOIs
Publication statusPublished - 1 Jan 2014

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