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Width asymptotics for a pair of Reinhardt domains

A. Aytuna, A. Rashkovskii, V. Zahariuta (2002)

Annales Polonici Mathematici

For complete Reinhardt pairs “compact set - domain” K ⊂ D in ℂⁿ, we prove Zahariuta’s conjecture about the exact asymptotics l n d s ( A K D ) - ( ( n ! s ) / τ ( K , D ) ) 1 / n , s → ∞, for the Kolmogorov widths d s ( A K D ) of the compact set in C(K) consisting of all analytic functions in D with moduli not exceeding 1 in D, τ(K,D) being the condenser pluricapacity of K with respect to D.

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