Geodesic
Width asymptotics for a pair of Reinhardt domains
A. Aytuna1 ; A. Rashkovskii2 ; V. Zahariuta3
1 Department of Mathematics Middle East Technical University Ankara, Turkey
2 Institute for Low Temperature Physics Kharkov, Ukraine
3 Rostov State University Rostov-na-Donu, Russia and Department of Mathematics Middle East Technical University Ankara, Turkey
Annales Polonici Mathematici, Tome 78 (2002) no. 1, pp. 31-38

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $D$.
DOI : 10.4064/ap78-1-4
Keywords: complete reinhardt pairs compact set domain subset mathbb prove zahariutas conjecture about exact asymptotics k sim bigl frac tau bigr quad infty kolmogorov widths k compact set consisting analytic functions moduli exceeding tau being condenser pluricapacity respect

A. Aytuna 1 ; A. Rashkovskii 2 ; V. Zahariuta 3

1 Department of Mathematics Middle East Technical University Ankara, Turkey
2 Institute for Low Temperature Physics Kharkov, Ukraine
3 Rostov State University Rostov-na-Donu, Russia and Department of Mathematics Middle East Technical University Ankara, Turkey 
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A. Aytuna; A. Rashkovskii; V. Zahariuta. Width asymptotics for
a pair of Reinhardt domains. Annales Polonici Mathematici, Tome 78 (2002) no. 1, pp. 31-38. doi: 10.4064/ap78-1-4

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