Extremal Structure of Convex Sets in Spaces Not Containing co.
V.E. Zizler, J.H.M. Whitfield (1988)
Mathematische Zeitschrift
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V.E. Zizler, J.H.M. Whitfield (1988)
Mathematische Zeitschrift
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H. Groemer (1983)
Monatshefte für Mathematik
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V.L. Klee jr. (1958)
Mathematische Zeitschrift
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Siegfried Helbig (1988)
Commentationes Mathematicae Universitatis Carolinae
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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 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 when the corresponding sequence of Kergin interpolation polynomials converges uniformly (on ) to the interpolated function as soon as it is holomorphic on a neighborhood of .). Extremal arrays on these ellipses are characterized in terms of the distribution of the points and the rate of convergence...
S. Kołodziej (1989)
Annales Polonici Mathematici
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J. Śladkowska (1983)
Annales Polonici Mathematici
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J. Zamorski (1958-1959)
Annales Polonici Mathematici
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Finnur Lárusson, Ragnar Sigurdsson (2005)
Annales Polonici Mathematici
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We establish disc formulas for the Siciak-Zahariuta extremal function of an arbitrary open subset of complex affine space. This function is also known as the pluricomplex Green function with logarithmic growth or a logarithmic pole at infinity. We extend Lempert's formula for this function from the convex case to the connected case.