On the homogeneous extremal function for the standard simplex

Autor

  • Mirosław Baran Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie, Wydział Matematyki, Fizyki i Nauk Technicznych

DOI:

https://doi.org/10.5604/01.3001.0012.8154

Słowa kluczowe:

homogeneous extremal function, convex stets

Abstrakt

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.

Statystyka pobrań

Statystyki pobrań nie są jeszcze dostępne

M. Baran, Siciak’s extremal function of convex sets in Cn, Ann. Polon. Math. 48 (3) (1988), 275–280.   Google Scholar

M. Baran, Plurisubharmonic extremal function and complex foliation for the complement of convex sets in Rn, Michigan Math. J. 39 (1992), 395–404.   Google Scholar

M. Baran, Homogeneous extremal function for a ball in R2, Ann. Polon. Math. 71 (1999), 141–150.   Google Scholar

M. Baran, Polynomial inequalities in Banach spaces, Banach Center Publications 107 (2015), 21–40.   Google Scholar

M.Klimek, Pluripotential Theory, London Mathematical Society Monographs New Series 6, Clarendon Press, Oxford, 1991.   Google Scholar

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.   Google Scholar

J. Siciak, Extremal plurisubharmonic functions in CN , Ann. Polon. Math. 39 (1981) 175-211.   Google Scholar

J. Siciak, Extremal Plurisubharmonic Functions and Capacities in Cn, Sophia Kokyuroku in Mathematics 14, (1982).   Google Scholar

Opublikowane

2018-12-27

Jak cytować

Baran, M. (2018). On the homogeneous extremal function for the standard simplex. Science, Technology and Innovation, 3(2), 35–42. https://doi.org/10.5604/01.3001.0012.8154

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