ISSN:
1573-8795
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let G and Ω. be two Radon domains in ℂ, let ϕ:ℂG-ℂΩ be a conformai mapping, and let Lτ, τ〉O be the level curves of the Green function of the domain ℂ ¯Ω. We completely describe the class of functions f, analytic in G, which can be approximated by polynomials of degree n{Pn} 1 ∞ such that $$\left| {f(Z) + P_n (Z)} \right| \leqslant const \cdot \rho [\varphi ({\rm Z}),L_{\begin{array}{*{20}c} 1 \\ n \\ \end{array} } ]^s ,Z \in \partial G$$ . It is shown that this class coincides with the “relative Holder class of order S,”, generated by Ω. For Ω=G and Ω={Z:|Z|〈1} one obtains V. K. Dzyadyk's approximation and the uniform approximation, respectively.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02427729
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