New PDF release: Analytic Capacity, the Cauchy Transform, and Non-homogeneous

By Xavier Tolsa

ISBN-10: 3319005952

ISBN-13: 9783319005959

This publication reports a few of the groundbreaking advances which were made concerning analytic means and its courting to rectifiability within the decade 1995–2005. The Cauchy rework performs a basic position during this region and is consequently one of many major topics coated. one other very important subject, that could be of autonomous curiosity for lots of analysts, is the so-called non-homogeneous Calderón-Zygmund concept, the improvement of which has been mostly prompted by means of the issues coming 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 services in metric and geometric phrases. Analytic means is a key software within the examine of this challenge. within the Nineteen Sixties Vitushkin conjectured that the detachable units that have finite size coincide with these that are simply unrectifiable. in addition, as a result of the functions to the idea of uniform rational approximation, he posed the query as to if analytic skill is semiadditive. This paintings provides 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, similar to the connection among rectifiability and the lifestyles of imperative 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 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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