Estimates of the Kolmogorov Widths of Classes of Analytic Functions Representable by Cauchy-Type Integrals. II - Romanyuk, V. S. (Ukrains’kyi Matematychnyi Zhurnal, 2001)
In normed spaces of functions analytic in the Jordan domain Ω⊂ℂ, we establish exact order estimates for the Kolmogorov widths of classes of functions that can be represented in Ω by Cauchy-type integrals along Γ = ∂Ω with densities f(·) such that \(f ° Ψ \in L_{β ,p}^Ψ (T)\) . Here, Ψ is a conformal mapping of \(C\backslash \overline Ω \) onto {w: |w| > 1}, and \(L_{β ,p}^Ψ (T)\) is a certain subset of infinitely differentiable functions on T = {w: |w| = 1}.