2017
Том 69
№ 9

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

Romanyuk V. S.

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Abstract

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 \(f \circ \Psi \in L_{\beta ,p}^\Psi (T)\) . Here, Ψ is a conformal mapping of \(C\backslash \overline \Omega \) onto {w: |w| > 1}, and \(L_{\beta ,p}^\Psi (T)\) is a certain subset of infinitely differentiable functions on T = {w: |w| = 1}.

English version (Springer): Ukrainian Mathematical Journal 53 (2001), no. 3, pp 395-406.

Citation Example: Romanyuk V. S. Estimates of the Kolmogorov Widths of Classes of Analytic Functions Representable by Cauchy-Type Integrals. II // Ukr. Mat. Zh. - 2001. - 53, № 3. - pp. 346-355.

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