Analytic capacity and approximation problems
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This article is published in Transactions of the American Mathematical Society.The article was published on 1972-09-01 and is currently open access. It has received 43 citations till now. The article focuses on the topics: Minimax approximation algorithm & Spouge's approximation.read more
Citations
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The theory of subnormal operators
TL;DR: In this paper, the elementary theory of subnormal operators on the unit circle is studied. But the authors do not discuss the structure theory for subnormal operator functions and bounded point evaluations.
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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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Painleve's problem and the semiadditivity of analytic capacity
TL;DR: In this paper, 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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Analytic capacity: discrete approach and curvature of measure
TL;DR: In this paper, the concept of curvature of a measure is introduced, which emerges naturally in the computations of the -norm of the Cauchy transform of this measure, and a lower bound on the analytic capacity, which uses the measure curvature and has, to this extent, a geometric nature, is obtained.
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Approximation in the mean by polynomials
TL;DR: For a positive measure AL with compact support in the complex plane C and for 1 < t < co, let pt(i) denote the closure in Lt(/i) of the polynomials in one complex variable as mentioned in this paper.
References
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The analytic capacity of sets in problems of approximation theory
TL;DR: In this article, the authors define the analytic capacity of sets and define the connection between the capacity of a set and measures, and give a generalization of the capacity analogue to the theorem on density points.
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Analytic Capacity and Rational Approximation
TL;DR: In this paper, the problem of rational approximation of integrals has been studied in the context of function algebra and function algebra methods, and applications of Vitushkin's theorem have been discussed.
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Positive length but zero analytic capacity
TL;DR: A simpler counterexample is given, and Vituskin's proof is compared to the authors', which is quite complicated and contains many typographical errors.