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Analytic capacity and measure
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TLDR
In this paper, the cauchy transform and Hausdorff measure are used to approximate the approximation of an approximation to a given function in terms of the number of nodes.Analytic capacityAbstract:
Analytic capacity.- The cauchy transform.- Hausdorff measure.- Some examples.- Applications to approximation.read more
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Rectifiable sets and the Traveling Salesman Problem
TL;DR: In this article, the authors give a necessary and sufficient condition for a given set K to lie in a rectifiable curve, which is the image of a finite interval under a Lipschitz mapping.
Journal ArticleDOI
Area distortion of quasiconformal mappings
TL;DR: In this paper, it has been shown that K-quasiconformal mappings are locally H51der continuous with exponent 1/K. The function is defined as follows:
Book
The Cauchy Transform
TL;DR: In this paper, the Cauchy transform as a function and as an operator are discussed. But the authors focus on the distribution function for Cauche transforms, not on the operator.
Journal ArticleDOI
Painlevé's problem and the semiadditivity of analytic capacity
TL;DR: In this article, it was shown that the analytic capacity of a compact set of positive measures can be characterized in terms of the curvature of the measures, and the authors deduced that Θ(E) is semiadditive.
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Quasiregular mappings in even dimensions
Tadeusz Iwaniec,Gaven Martin +1 more
TL;DR: In this paper, the authors present removalability theorems for quasiregular mappings in Lnm (i2, A n) and LP(R n) for the 4-dimensional case.
References
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Book
The Theory of Cluster Sets
E. F. Collingwood,A. J. Lohwater +1 more
TL;DR: The theory of cluster sets is a branch of topological analysis which has made great strides in recent years as discussed by the authors, with particular reference to boundary behaviour such as the theory of prime ends under conformal mapping.
Journal ArticleDOI
Sur la continuité des fonctions analytiques singulières
TL;DR: The Bulletin de la S. M. F. as mentioned in this paper implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.html).