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1999 | 72 | 3 | 285-305
Tytuł artykułu

On the multivariate transfinite diameter

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.
Rocznik
Tom
72
Numer
3
Strony
285-305
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-06-25
poprawiono
1999-10-11
poprawiono
1999-11-10
Twórcy
autor
  • Department of Mathematics, University of Toronto, M5S 3G3, Toronto, Ontario, Canada
  • Laboratoire de Mathématiques E. Picard, UFR MIG, Université Paul Sabatier, 31062 Toulouse Cedex, France
Bibliografia
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  • [BT2] E. Bedford and B. A. Taylor, Fine topology, Šilov boundary, and $(dd^c)^n$, J. Funct. Anal. 72 (1987), 225-251.
  • [Blo] Z. Błocki, The equilibrium measure for product subsets of $ℂ^n$, preprint, 1999.
  • [Bl] T. Bloom, Some applications of the Robin function to multivariable approximation theory, J. Approx. Theory 92 (1998), 1-21.
  • [BBCL] T. Bloom, L. Bos, C. Christensen and N. Levenberg, Polynomial interpolation of holomorphic functions in ℂ and $ℂ^n$, Rocky Mountain J. Math. 22 (1992), 441-470.
  • [BC] T. Bloom and J.-P. Calvi, On multivariate minimal polynomials, preprint, 1999.
  • [Bo] L. Bos, A characteristic of points in $ℝ^2$ having a Lebesgue function of exponential growth, J. Approx. Theory 56 (1989), 316-329.
  • [Go] G. M. Goluzin, Geometric Theory of a Function of a Complex Variable, Amer. Math. Soc., Providence, 1969.
  • [Je] M. Jędrzejowski, The homogeneous transfinite diameter of a compact subset of $ℂ^n$, Ann. Polon. Math. 55 (1991), 191-205.
  • [Kl] M. Klimek, Pluripotential Theory, Oxford Univ. Press, Oxford, 1991.
  • [Kl2] M. Klimek, Metrics associated with extremal plurisubharmonic functions, Proc. Amer. Math. Soc. 125 (1995), 2763-2770.
  • [Le] N. Levenberg, Capacities in Several Complex Variables, thesis, University of Michigan, 1984.
  • [LT] N. Levenberg and B. A. Taylor, Comparison of capacities in $ℂ^n$, in: Lectures Notes in Math. 1094, Springer, 1984, 162-172.
  • [NZ] T. V. Nguyen et A. Zeriahi, Familles de polynômes presque partout bornées, Bull. Sci. Math. (2) 107 (1983), 81-91.
  • [Ra] T. Ransford, Potential Theory in the Complex Plane, Cambridge Univ. Press, Cambridge, 1995.
  • [SS] M. Schiffer and J. Siciak, Transfinite diameter and analytic continuation of functions of two complex variables, in: Studies in Math. Analysis and Related Topics, Stanford Univ. Press, 1962, 341-358.
  • [Sh] V. P. Sheĭnov, Invariant form of Pólya's inequalities, Siberian Math. J. 14 (1973), 138-145.
  • [Si1] J. Siciak, Extremal plurisubharmonic functions on $ℂ^N$, Ann. Polon. Math. 39 (1981), 175-211.
  • [Si2] J. Siciak, A remark on Tchebysheff polynomials in $ℂ^n$, Univ. Iagell. Acta Math. 35 (1997), 37-45.
  • [Za] V. P. Zaharjuta [V. P. Zakharyuta], Transfinite diameter, Chebyshev constants, and capacity for compacta in $ℂ^n$, Math. USSR-Sb. 25 (1975), 350-364.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv72z3p285bwm
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