Analytic Capacity, the Cauchy Transform, and Non-homogeneous by Xavier Tolsa PDF

By Xavier Tolsa

This e-book experiences a number of the groundbreaking advances which were made concerning analytic means and its courting to rectifiability within the decade 1995–2005. The Cauchy remodel performs a basic position during this region and is hence one of many major matters coated. one other very important subject, that could be of self sufficient curiosity for plenty of analysts, is the so-called non-homogeneous Calderón-Zygmund thought, the improvement of which has been principally inspired via the issues bobbing up in reference to analytic capability. The Painlevé challenge, which was once first posed round 1900, is composed find an outline of the detachable singularities for bounded analytic services in metric and geometric phrases. Analytic potential is a key software within the learn of this challenge. within the Sixties Vitushkin conjectured that the detachable units that have finite size coincide with these that are in basic terms unrectifiable. in addition, end result of the functions to the idea of uniform rational approximation, he posed the query to whether analytic ability is semiadditive. This paintings offers complete proofs of Vitushkin’s conjecture and of the semiadditivity of analytic capability, either one of which remained open difficulties until eventually very lately. different similar questions also are mentioned, akin to the connection among rectifiability and the lifestyles of important values for the Cauchy transforms and different singular integrals. The ebook is basically self-contained and will be available for graduate scholars in research, in addition to a priceless source for researchers.

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Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón–Zygmund Theory: 307 (Progress in Mathematics) by Xavier Tolsa

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