Displaying similar documents to “The Siciak-Zahariuta extremal function as the envelope of disc functionals”

Siciak-Zahariuta extremal functions and polynomial hulls

Finnur Lárusson, Ragnar Sigurdsson (2007)

Annales Polonici Mathematici

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We use our disc formula for the Siciak-Zahariuta extremal function to characterize the polynomial hull of a connected compact subset of complex affine space in terms of analytic discs.

Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties

Barbara Drinovec Drnovšek, Franc Forstnerič (2012)

Annales Polonici Mathematici

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We establish plurisubharmonicity of envelopes of certain classical disc functionals on locally irreducible complex spaces, thereby generalizing the corresponding results for complex manifolds. We also find new formulae expressing the Siciak-Zaharyuta extremal function of an open set in a locally irreducible affine algebraic variety as the envelope of certain disc functionals, similarly to what has been done for open sets in ℂⁿ by Lempert and by Lárusson and Sigurdsson.

Estimating the extremal index through the tail dependence concept

Marta Ferreira (2015)

Discussiones Mathematicae Probability and Statistics

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The extremal index Θ is an important parameter in extreme value analysis when extending results from independent and identically distributed sequences to stationary ones. A connection between the extremal index and the tail dependence coefficient allows the introduction of new estimators. The proposed ones are easy to compute and we analyze their performance through a simulation study. Comparisons with other existing methods are also presented. Case studies within environment are considered...

The distribution of extremal points for Kergin interpolations : real case

Thomas Bloom, Jean-Paul Calvi (1998)

Annales de l'institut Fourier

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We show that a convex totally real compact set in ℂ n admits an extremal array for Kergin interpolation if and only if it is a totally real ellipse. (An array is said to be extremal for K when the corresponding sequence of Kergin interpolation polynomials converges uniformly (on K ) to the interpolated function as soon as it is holomorphic on a neighborhood of K .). Extremal arrays on these ellipses are characterized in terms of the distribution of the points and the rate of convergence...

Siciak's extremal function in complex and real analysis

W. Pleśniak (2003)

Annales Polonici Mathematici

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The Siciak extremal function establishes an important link between polynomial approximation in several variables and pluripotential theory. This yields its numerous applications in complex and real analysis. Some of them can be found on a rich list drawn up by Klimek in his well-known monograph "Pluripotential Theory". The purpose of this paper is to supplement it by applications in constructive function theory.