Read e-book online Analytic Capacity, the Cauchy Transform, and Non-homogeneous PDF

By Xavier Tolsa

ISBN-10: 3319005952

ISBN-13: 9783319005959

This publication reports a few of the groundbreaking advances which were made concerning analytic potential and its dating to rectifiability within the decade 1995–2005. The Cauchy rework performs a primary function during this zone and is therefore one of many major topics lined. one other vital subject, that may be of autonomous curiosity for lots of analysts, is the so-called non-homogeneous Calderón-Zygmund concept, the improvement of which has been principally inspired by way of the issues coming up in reference to analytic ability. The Painlevé challenge, which was once first posed round 1900, is composed to find an outline of the detachable singularities for bounded analytic services in metric and geometric phrases. Analytic means is a key instrument 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 simple terms unrectifiable. in addition, due to the purposes to the idea of uniform rational approximation, he posed the query as to if analytic potential is semiadditive. This paintings offers complete proofs of Vitushkin’s conjecture and of the semiadditivity of analytic ability, either one of which remained open difficulties till very lately. different similar questions also are mentioned, similar to the connection among rectifiability and the lifestyles of central values for the Cauchy transforms and different singular integrals. The e-book is basically self-contained and will be available for graduate scholars in research, in addition to a important 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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