The homogeneous transfinite diameter of a compact subset of ℂ N

Mieczysław Jędrzejowski

Annales Polonici Mathematici (1991)

  • Volume: 55, Issue: 1, page 191-205
  • ISSN: 0066-2216

Abstract

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Let K be a compact subset of ℂ N . A sequence of nonnegative numbers defined by means of extremal points of K with respect to homogeneous polynomials is proved to be convergent. Its limit is called the homogeneous transfinite diameter of K. A few properties of this diameter are given and its value for some compact subsets of ℂ N is computed.

How to cite

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Mieczysław Jędrzejowski. "The homogeneous transfinite diameter of a compact subset of $ℂ^N$." Annales Polonici Mathematici 55.1 (1991): 191-205. <http://eudml.org/doc/262363>.

@article{MieczysławJędrzejowski1991,
abstract = {Let K be a compact subset of $ℂ^N$. A sequence of nonnegative numbers defined by means of extremal points of K with respect to homogeneous polynomials is proved to be convergent. Its limit is called the homogeneous transfinite diameter of K. A few properties of this diameter are given and its value for some compact subsets of $ℂ^N$ is computed.},
author = {Mieczysław Jędrzejowski},
journal = {Annales Polonici Mathematici},
keywords = {Chebyshev constant; homogeneous polynomials; extremal points; compact subset; homogeneous transfinite diameter},
language = {eng},
number = {1},
pages = {191-205},
title = {The homogeneous transfinite diameter of a compact subset of $ℂ^N$},
url = {http://eudml.org/doc/262363},
volume = {55},
year = {1991},
}

TY - JOUR
AU - Mieczysław Jędrzejowski
TI - The homogeneous transfinite diameter of a compact subset of $ℂ^N$
JO - Annales Polonici Mathematici
PY - 1991
VL - 55
IS - 1
SP - 191
EP - 205
AB - Let K be a compact subset of $ℂ^N$. A sequence of nonnegative numbers defined by means of extremal points of K with respect to homogeneous polynomials is proved to be convergent. Its limit is called the homogeneous transfinite diameter of K. A few properties of this diameter are given and its value for some compact subsets of $ℂ^N$ is computed.
LA - eng
KW - Chebyshev constant; homogeneous polynomials; extremal points; compact subset; homogeneous transfinite diameter
UR - http://eudml.org/doc/262363
ER -

References

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  10. [10] M. Schiffer and J. Siciak, Transfinite diameter and analytic continuation of functions of two complex variables, Technical Report, Stanford 1961. Zbl0113.06202
  11. [11] J. Siciak, On some extremal functions and their applications in the theory of analytic functions of several complex variables, Trans. Amer. Math. Soc. 105 (2) (1962), 322-357. Zbl0111.08102
  12. [12] J. Siciak, Extremal plurisubharmonic functions and capacities in ℂ n , Sophia Kokyuroku in Math. 14, Sophia University, Tokyo 1982. Zbl0579.32025
  13. [13] J. Siciak, Families of polynomials and determining measures, Ann. Fac. Sci. Toulouse 9 (2) (1988), 193-211. Zbl0634.31005
  14. [14] V. P. Zakharyuta, Transfinite diameter, Chebyshev constants and a capacity of a compact set in ℂ n , Mat. Sb. 96 (138) (3) (1975), 374-389 (in Russian). Zbl0324.32009

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