Download e-book for iPad: Analytic Capacity, the Cauchy Transform, and Non-homogeneous by Xavier Tolsa

By Xavier Tolsa

This e-book reviews the various groundbreaking advances which have been made concerning analytic potential and its courting to rectifiability within the decade 1995–2005. The Cauchy remodel performs a basic position during this zone and is for that reason one of many major matters lined. one other vital subject, that may be of autonomous curiosity for plenty of analysts, is the so-called non-homogeneous Calderón-Zygmund conception, the advance of which has been principally encouraged via the issues bobbing 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 Nineteen Sixties Vitushkin conjectured that the detachable units that have finite size coincide with these that are basically unrectifiable. additionally, end result of the purposes to the speculation of uniform rational approximation, he posed the query to whether analytic means is semiadditive. This paintings provides complete proofs of Vitushkin’s conjecture and of the semiadditivity of analytic ability, either one of which remained open difficulties until eventually very lately. different similar questions also are mentioned, similar to the connection among rectifiability and the lifestyles of significant values for the Cauchy transforms and different singular integrals. The e-book is basically self-contained and will be obtainable for graduate scholars in research, in addition to a invaluable 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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