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

By Xavier Tolsa

This ebook reviews a number of the groundbreaking advances which were made concerning analytic ability and its courting to rectifiability within the decade 1995–2005. The Cauchy remodel performs a basic function during this sector and is consequently one of many major topics lined. one other very important subject, that may be of self sufficient curiosity for plenty of analysts, is the so-called non-homogeneous Calderón-Zygmund conception, the advance of which has been principally inspired via 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 features in metric and geometric phrases. Analytic means is a key device 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 in basic terms unrectifiable. furthermore, as a result functions to the speculation of uniform rational approximation, he posed the query as to if analytic skill 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 till very lately. different similar questions also are mentioned, reminiscent of the connection among rectifiability and the life of central values for the Cauchy transforms and different singular integrals. The booklet is essentially self-contained and will be available for graduate scholars in research, in addition to a beneficial 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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