Width asymptotics for a pair of Reinhardt domains

Volume 78 / 2002

A. Aytuna, A. Rashkovskii, V. Zahariuta Annales Polonici Mathematici 78 (2002), 31-38 MSC: 32A07, 32U20. DOI: 10.4064/ap78-1-4

Abstract

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 $D$.

Authors

  • A. AytunaDepartment of Mathematics
    Middle East Technical University
    Ankara, Turkey
    e-mail
  • A. RashkovskiiInstitute for Low Temperature Physics
    Kharkov, Ukraine
    e-mail
  • V. ZahariutaRostov State University
    Rostov-na-Donu, Russia
    and
    Department of Mathematics
    Middle East Technical University
    Ankara, Turkey
    e-mail

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