Width asymptotics for a pair of Reinhardt domains
Tom 78 / 2002
Annales Polonici Mathematici 78 (2002), 31-38
MSC: 32A07, 32U20.
DOI: 10.4064/ap78-1-4
Streszczenie
For complete Reinhardt pairs “compact set – domain” $K \subset D$ in ${\mathbb C}^n$, we prove Zahariuta's conjecture about the exact asymptotics $$ \ln d_s(A_K^D) \sim -\Bigl(\frac{n!\,s}{\tau(K,D)} \Bigr)^{1//n},\quad\ s\to\infty, $$ 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 $D$, $\tau(K,D)$ being the condenser pluricapacity of $K$ with respect to $D$.
