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Analytic capacity

In the mathematical discipline of complex analysis, the analytic capacity of a compact subset K of the complex plane is a number that denotes "how big" a bounded analytic function on C \ K can become. Roughly speaking, γ(K) measures the size of the unit ball of the space of bounded analytic functions outside K.

Measurement, Analytic capacity in terms of Hausdorff dimension & Definition

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Analytic capacity in terms of Hausdorff dimension

Hausdorff dimensionHausdorff measureA. G. VitushkinJohn B. GarnettAnatoli Vitushkin
10 related topics

Definition

CompactFunctionsOpenSupremum
4 related topics

Removable sets and Painlevé's problem

Riemann's theorem for removable singularitiesSingletonPaul Painlevé
3 related topics

Ahlfors function

Montel's theorem
1 related topics

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Definition

Removable sets and Painlevé's problem

Ahlfors function

Analytic capacity in terms of Hausdorff dimension

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Analytic capacity

Nodes32
Edges31
Triples63
Avg. degree1.94
Density0.0625
Components1

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Analytic capacity

Top relations

related to References · 35
Analytic capacity → Amer, Birkhäuser Basel, Cambridge University Press, Cauchy Integral, Cauchy Transform, David, Euclidean, Garnett, Geometry, Hervé, Iberoam, ISBN, James, Lecture Notes, Math, Mathematics, Mattila, Menger Curvature, Non-homogeneous Calderón, Pajot
related to Positive length but zero analytic capacity · 16
Analytic capacity → Cantor, Garnett, Given, H1, Hausdorff, However, In, John, K0, K1, Kn, Let K0, Take, Then, This, Vitushkin
related to Removable sets and Painlevé's problem · 7
Analytic capacity → By Riemann's, However, It, Paul Painlevé, The, This, Which
related to Definition · 4
Analytic capacity → Further, Here, Let, Then
is a · 1
Analytic capacity → purely complex-analytic concept

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analytic capacity bounded compact displaystyle conjecture set function infty functions removable length vitushkin's h1 positive ahlfors however subset denotes isbn

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SubjectPredicateObjectConfidenceSrc
Analytic capacityis apurely complex-analytic concept0.90text
Analytic capacityrelated to DefinitionLet0.60section
Analytic capacityrelated to DefinitionThen0.60section
Analytic capacityrelated to DefinitionHere0.60section
Analytic capacityrelated to DefinitionFurther0.60section
Analytic capacityrelated to Positive length but zero analytic capacityGiven0.60section
Analytic capacityrelated to Positive length but zero analytic capacityHausdorff0.60section
Analytic capacityrelated to Positive length but zero analytic capacityH10.60section
Analytic capacityrelated to Positive length but zero analytic capacityHowever0.60section
Analytic capacityrelated to Positive length but zero analytic capacityVitushkin0.60section
Analytic capacityrelated to Positive length but zero analytic capacityJohn0.60section
Analytic capacityrelated to Positive length but zero analytic capacityGarnett0.60section

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