Width asymptotics for a pair of Reinhardt domains

• Autorzy: A. Aytuna , A. Rashkovskii , V. Zahariuta
• Języki publikacji: EN

Abstrakty

EN

For complete Reinhardt pairs "compact set - domain" K ⊂ D in ℂⁿ, we prove Zahariuta's conjecture about the exact asymptotics
$ln d_s(A_K^D) ~ -((n!s)/τ(K,D))^{1/n}$, 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.

Kategorie tematyczne

• 32A07: Special domains (Reinhardt, Hartogs, circular, tube)
• 32U20: Capacity theory and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2002
• Tom: 78
• Numer: 1
• Strony: 31-38

Daty

wydano

2002

Twórcy

autor

A. Aytuna

• Department of Mathematics, Middle East Technical University, Ankara, Turkey

autor

A. Rashkovskii

• Institute for Low Temperature Physics, Kharkov, Ukraine

autor

V. Zahariuta

• Rostov State University, Rostov-na-Donu, Russia
• Department of Mathematics, Middle East Technical University, Ankara, Turkey

Identyfikatory

DOI

10.4064/ap78-1-4