Estimates of the Kolmogorov Widths of Classes of Analytic Functions Representable by Cauchy-Type Integrals. I

Abstract

In the Banach space of functions analytic in a Jordan domain $\Omega \subset \mathbb{C}$ , we establish order estimates for the Kolmogorov widths of certain classes of functions that can be represented in Ω by Cauchy-type integrals along the rectifiable curve Γ = ∂Ω and can be analytically continued to Ω′ ⊃ Ω or to $\mathbb{C}$