On the homogeneous extremal function for the standard simplex

• Autorzy: Baran M.

Identyfikatory

DOI

10.5604/01.3001.0012.8154

• Języki publikacji: EN

Abstrakty

EN

In this paper an explicit formula for the homogeneous Siciak’s extremal function is computed in the case of standard simplex in RN. There are discussed some problems related to this result. In particular, there is proved a version of Klimek’s type theorem for the homogeneous extremal function.

Słowa kluczowe

EN

extremal function; standard simplex; convex set

PL

funkcja ekstremalna; standardowy sympleks; wypukły zestaw

• Wydawca: Państwowa Wyższa Szkoła Zawodowa w Tarnowie
• Czasopismo: Science, Technology and Innovation
• Rocznik: 2018
• Tom: Vol. 3, no. 2
• Strony: 35--42
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Baran M.

• State Higher Vocational School in Tarnow, Mickiewicza 8, 33-100 Tarnów, Poland

Bibliografia

• [1] M. Baran, Siciak’s extremal function of convex sets in Cn, Ann. Polon. Math. 48 (3) (1988), 275–280.
• [2] M. Baran, Plurisubharmonic extremal function and complex foliation for the complement of convex sets in Rn, Michigan Math. J. 39 (1992), 395–404.
• [3] M. Baran, Homogeneous extremal function for a ball in R2, Ann. Polon. Math. 71 (1999), 141–150.
• [4] M. Baran, Polynomial inequalities in Banach spaces, Banach Center Publications 107 (2015), 21–40.
• [5] M. Klimek, Pluripotential Theory, London Mathematical Society Monographs New Series 6, Clarendon Press, Oxford, 1991.
• [6] J. Siciak, On some extremal functions and their applications in the theory of analytic functions of several complex variables, Trans. Amer. Math. Soc. 105 (1962), 322–357.
• [7] J. Siciak, Extremal plurisubharmonic functions in CN, Ann. Polon. Math. 39 (1981) 175-211.
• [8] J. Siciak, Extremal Plurisubharmonic Functions and Capacities in Cn, Sophia Kokyuroku in Mathematics 14, (1982).