Alexander’s projective capacity for polydisks and ellipsoids in ℂ N

Mieczysław Jędrzejowski

Annales Polonici Mathematici (1995)

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

Abstract

top
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.

How to cite

top

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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.