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

By Xavier Tolsa

ISBN-10: 3319005952

ISBN-13: 9783319005959

This ebook experiences a few of the groundbreaking advances which were made relating to analytic ability and its dating to rectifiability within the decade 1995–2005. The Cauchy rework performs a primary position during this zone and is therefore one of many major topics coated. one other vital subject, that could be of self sustaining curiosity for plenty of analysts, is the so-called non-homogeneous Calderón-Zygmund thought, the improvement of which has been principally prompted by means of the issues bobbing up in reference to analytic potential. The Painlevé challenge, which used to be first posed round 1900, is composed find an outline of the detachable singularities for bounded analytic capabilities in metric and geometric phrases. Analytic ability 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 merely unrectifiable. furthermore, as a result functions to the idea of uniform rational approximation, he posed the query to whether analytic capability 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, corresponding to the connection among rectifiability and the lifestyles of central values for the Cauchy transforms and different singular integrals. The publication is essentially self-contained and may be available 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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