# Alexander’s projective capacity for polydisks and ellipsoids in ${\u2102}^{N}$

Annales Polonici Mathematici (1995)

- Volume: 62, Issue: 3, page 245-264
- ISSN: 0066-2216

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topMieczysław Jędrzejowski. "Alexander’s projective capacity for polydisks and ellipsoids in $ℂ^N$." Annales Polonici Mathematici 62.3 (1995): 245-264. <http://eudml.org/doc/262759>.

@article{MieczysławJędrzejowski1995,

abstract = {Alexander’s projective capacity for the polydisk and the ellipsoid in $ℂ^N$ is computed. Sharper versions of two inequalities concerning this capacity and some other capacities in $ℂ^N$ are given. A sequence of orthogonal polynomials with respect to an appropriately defined measure supported on a compact subset K in $ℂ^N$ is proved to have an asymptotic behaviour in $ℂ^N$ similar to that of the Siciak homogeneous extremal function associated with K.},

author = {Mieczysław Jędrzejowski},

journal = {Annales Polonici Mathematici},

keywords = {ellipsoid; projective capacity; extremal function; extremal functions; polydisk; orthogonal polynomials},

language = {eng},

number = {3},

pages = {245-264},

title = {Alexander’s projective capacity for polydisks and ellipsoids in $ℂ^N$},

url = {http://eudml.org/doc/262759},

volume = {62},

year = {1995},

}

TY - JOUR

AU - Mieczysław Jędrzejowski

TI - Alexander’s projective capacity for polydisks and ellipsoids in $ℂ^N$

JO - Annales Polonici Mathematici

PY - 1995

VL - 62

IS - 3

SP - 245

EP - 264

AB - Alexander’s projective capacity for the polydisk and the ellipsoid in $ℂ^N$ is computed. Sharper versions of two inequalities concerning this capacity and some other capacities in $ℂ^N$ are given. A sequence of orthogonal polynomials with respect to an appropriately defined measure supported on a compact subset K in $ℂ^N$ is proved to have an asymptotic behaviour in $ℂ^N$ similar to that of the Siciak homogeneous extremal function associated with K.

LA - eng

KW - ellipsoid; projective capacity; extremal function; extremal functions; polydisk; orthogonal polynomials

UR - http://eudml.org/doc/262759

ER -

## References

top- [1] H. Alexander, Projective capacity, in: Conference on Several Complex Variables, Ann. of Math. Stud. 100, Princeton Univ. Press, 1981, 3-27.
- [2] U. Cegrell and S. Kołodziej, An identity between two capacities, Univ. Iagel. Acta Math. 30 (1993), 155-157. Zbl0837.31004
- [3] M. Jędrzejowski, The homogeneous transfinite diameter of a compact subset of ${\u2102}^{N}$, Ann. Polon. Math. 55 (1991), 191-205. Zbl0748.31008
- [4] J. Siciak, On an extremal function and domains of convergence of series of homogeneous polynomials, Ann. Polon. Math. 10 (1961), 297-307. Zbl0192.18102
- [5] 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. Zbl0111.08102
- [6] J. Siciak, Extremal Plurisubharmonic Functions and Capacities in ${\u2102}^{n}$, Sophia Kokyuroku in Math. 14, Sophia University, Tokyo, 1982.
- [7] J. Siciak, Families of polynomials and determining measures, Ann. Fac. Sci. Toulouse 9 (1988), 193-211. Zbl0634.31005
- [8] A. Zériahi, Capacité, constante de Čebyšev et polynômes orthogonaux associés à un compact de ${\u2102}^{n}$, Bull. Sci. Math. (2) 109 (1985), 325-335. Zbl0583.31006

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