On the multivariate transfinite diameter

 Access to full text

 Full (PDF)

1. [Ba] M. Baran, Conjugate norms in ${ℂ}^n$ and related geometrical problems, Dissertationes Math. 378 (1998). 
2. [BT] E. Bedford and B. A. Taylor, Plurisubharmonic functions with logarithmic singularities, Ann. Inst. Fourier (Grenoble) 38 (1988), no. 4, 133-171. Zbl0626.32022
3. [BT2] E. Bedford and B. A. Taylor, Fine topology, Šilov boundary, and ${\left(d{d}^c\right)}^n$, J. Funct. Anal. 72 (1987), 225-251. Zbl0677.31005
4. [Blo] Z. Błocki, The equilibrium measure for product subsets of ${ℂ}^n$, preprint, 1999. 
5. [Bl] T. Bloom, Some applications of the Robin function to multivariable approximation theory, J. Approx. Theory 92 (1998), 1-21. Zbl0896.31003
6. [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. Zbl0763.32009
7. [BC] T. Bloom and J.-P. Calvi, On multivariate minimal polynomials, preprint, 1999. 
8. [Bo] L. Bos, A characteristic of points in ${ℝ}^2$ having a Lebesgue function of exponential growth, J. Approx. Theory 56 (1989), 316-329. Zbl0675.41013
9. [Go] G. M. Goluzin, Geometric Theory of a Function of a Complex Variable, Amer. Math. Soc., Providence, 1969. Zbl0183.07502
10. [Je] M. Jędrzejowski, The homogeneous transfinite diameter of a compact subset of ${ℂ}^n$, Ann. Polon. Math. 55 (1991), 191-205. Zbl0748.31008
11. [Kl] M. Klimek, Pluripotential Theory, Oxford Univ. Press, Oxford, 1991. 
12. [Kl2] M. Klimek, Metrics associated with extremal plurisubharmonic functions, Proc. Amer. Math. Soc. 125 (1995), 2763-2770. Zbl0935.32028
13. [Le] N. Levenberg, Capacities in Several Complex Variables, thesis, University of Michigan, 1984. 
14. [LT] N. Levenberg and B. A. Taylor, Comparison of capacities in ${ℂ}^n$, in: Lectures Notes in Math. 1094, Springer, 1984, 162-172. 
15. [NZ] T. V. Nguyen et A. Zeriahi, Familles de polynômes presque partout bornées, Bull. Sci. Math. (2) 107 (1983), 81-91. Zbl0523.32011
16. [Ra] T. Ransford, Potential Theory in the Complex Plane, Cambridge Univ. Press, Cambridge, 1995. 
17. [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. 
18. [Sh] V. P. Sheĭnov, Invariant form of Pólya's inequalities, Siberian Math. J. 14 (1973), 138-145. 
19. [Si1] J. Siciak, Extremal plurisubharmonic functions on ${ℂ}^N$, Ann. Polon. Math. 39 (1981), 175-211. 
20. [Si2] J. Siciak, A remark on Tchebysheff polynomials in ${ℂ}^n$, Univ. Iagell. Acta Math. 35 (1997), 37-45. Zbl0951.32011
21. [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.