On approximation by special analytic polyhedral pairs

• Autorzy: V. Zahariuta
• Języki publikacji: EN

Abstrakty

EN

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 → ℂⁿ, n = dimΩ. This problem is closely connected with the problem of approximation of the pluripotential ω(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.

Kategorie tematyczne

• 32A07: Special domains (Reinhardt, Hartogs, circular, tube)
• 32U20: Capacity theory and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2003
• Tom: 80
• Numer: 1
• Strony: 243-256

Daty

wydano

2003

Twórcy

autor

V. Zahariuta

• Sabanci University, 81474 Tuzla, Istanbul, Turkey
• Middle East Technical University, Ankara, Turkey

Identyfikatory

DOI

10.4064/ap80-0-22