Capacities associated to the Siciak extremal function
S. Kołodziej (1989)
Annales Polonici Mathematici
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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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S. R. Kulkarni, M. K. Aouf, S. B. Joshi (1994)
Matematički Vesnik
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E. T. Davies (1972)
Colloquium Mathematicae
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Kazimierz Włodarczyk (1985)
Annales Polonici Mathematici
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W. Janowski (1970)
Annales Polonici Mathematici
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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...
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.
Iovanov, Miodrag (2004)
Acta Universitatis Apulensis. Mathematics - Informatics
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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.
B. Platynowicz (1984)
Matematički Vesnik
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Siegfried Helbig (1988)
Commentationes Mathematicae Universitatis Carolinae
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Marcin Marciniak (2010)
Banach Center Publications
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The paper is devoted to the problem of classification of extremal positive linear maps acting between 𝔅(𝒦) and 𝔅(ℋ) where 𝒦 and ℋ are Hilbert spaces. It is shown that every positive map with the property that rank ϕ(P) ≤ 1 for any one-dimensional projection P is a rank 1 preserver. This allows us to characterize all decomposable extremal maps as those which satisfy the above condition. Further, we prove that every extremal positive map which is 2-positive turns out to be automatically...