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9783319345444 - Xavier Tolsa: Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón-Zygmund Theory
1
Xavier Tolsa (?):

Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón-Zygmund Theory (?)

ISBN: 9783319345444 (?) or 3319345443, in english, New

ETB 4 (Fr. 125.40)¹ + Shipping: ETB 0 (Fr. 15.00)¹ = ETB 4 (Fr. 140.40)¹(without obligation)
plus shipping, Versandfertig innert 3 Wochen
From Seller/Antiquarian
Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón-Zygmund Theory, This book studies some of the groundbreaking advances that have been made regarding analytic capacity and its relationship to rectifiability in the decade 19952005. The Cauchy transform plays a fundamental role in this area and is accordingly one of the main subjects covered. Another important topic, which may be of independent interest for many analysts, is the so-called non-homogeneous Calderón-Zygmund theory, the development of which has been largely motivated by the problems arising in connection with analytic capacity. The Painlevé problem, which was first posed around 1900, consists in finding a description of the removable singularities for bounded analytic functions in metric and geometric terms. Analytic capacity is a key tool in the study of this problem. In the 1960s Vitushkin conjectured that the removable sets which have finite length coincide with those which are purely unrectifiable. Moreover, because of the applications to the theory of uniform rational approximation, he posed the question as to whether analytic capacity is semiadditive. This work presents full proofs of Vitushkins conjecture and of the semiadditivity of analytic capacity, both of which remained open problems until very recently. Other related questions are also discussed, such as the relationship between rectifiability and the existence of principal values for the Cauchy transforms and other singular integrals. The book is largely self-contained and should be accessible for graduate students in analysis, as well as a valuable resource for researchers.
Seller order number: 46025363
Platform order number Buch.ch: 029a4b53a96f80593b231068bf105d 10
Category: Bücher / Fremdsprachige Bücher / Englische Bücher
Keywords: Bücher
Data from 08/03/2016 19:00h
ISBN (alternative notations): 3-319-34544-3, 978-3-319-34544-4
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