1Department of Mathematics Middle East Technical University Ankara, Turkey 2Institute for Low Temperature Physics Kharkov, Ukraine 3Rostov 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
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 $D$.
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
Affiliations des auteurs :
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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author = {A. Aytuna and A. Rashkovskii and V. Zahariuta},
title = {Width asymptotics for
a pair of {Reinhardt} domains},
journal = {Annales Polonici Mathematici},
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year = {2002},
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doi = {10.4064/ap78-1-4},
language = {en},
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a pair of Reinhardt domains
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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
