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Abstract

For bounded logarithmically convex Reinhardt pairs “compact set – domain” $(K,D)$ we solve positively the problem on simultaneous approximation of such a pair by a pair of special analytic polyhedra, generated by the same polynomial mapping $f: D \to {\mathbb C}^n,$ $n = \mathop {\rm dim}\nolimits {\mit \Omega }.$ This problem is closely connected with the problem of approximation of the pluripotential $\omega (D,K;z)$ by pluripotentials with a finite set of isolated logarithmic singularities ([23, 24]). The latter problem has been solved recently for arbitrary pluriregular pairs “compact set – domain” $(K,D)$ by Poletsky [12] and S. Nivoche [10, 11], while the first one is still open in the general case.