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A constructive description of Hölder classes on closed Jordan curves. / Shirokov, N. A.
в: Journal of Soviet Mathematics, Том 37, № 5, 06.1987, стр. 1306-1322.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - A constructive description of Hölder classes on closed Jordan curves
AU - Shirokov, N. A.
PY - 1987/6
Y1 - 1987/6
N2 - Let Γ be a closed, Jordan, rectifiable curve, whose are length is commensurable with its subtending chord, let a ε int Γ, and let Rn(a) be the set of rational functions of degree ≤n, having a pole perhaps only at the point a. Let Λα(Γ), 0 < α < 1, be the Hölder class on Γ. One constructs a system of weights γn(z) > 0 on Γ such that f∈Λα(Γ) if and only if for any nonnegative integer n there exists a function Rn, Rn ε Rn(a) such that |f(z) - Rn(z)| ≤ cf·γn(z), z ε Γ. It is proved that the weights γn cannot be expressed simply in terms of ρ1+/n(z) and ρ1-/n(z), the distances to the level lines of the moduli of the conformal mappings of ext Γ and int Γ on {Mathematical expression}.
AB - Let Γ be a closed, Jordan, rectifiable curve, whose are length is commensurable with its subtending chord, let a ε int Γ, and let Rn(a) be the set of rational functions of degree ≤n, having a pole perhaps only at the point a. Let Λα(Γ), 0 < α < 1, be the Hölder class on Γ. One constructs a system of weights γn(z) > 0 on Γ such that f∈Λα(Γ) if and only if for any nonnegative integer n there exists a function Rn, Rn ε Rn(a) such that |f(z) - Rn(z)| ≤ cf·γn(z), z ε Γ. It is proved that the weights γn cannot be expressed simply in terms of ρ1+/n(z) and ρ1-/n(z), the distances to the level lines of the moduli of the conformal mappings of ext Γ and int Γ on {Mathematical expression}.
UR - http://www.scopus.com/inward/record.url?scp=34250109551&partnerID=8YFLogxK
U2 - 10.1007/BF01327040
DO - 10.1007/BF01327040
M3 - Article
AN - SCOPUS:34250109551
VL - 37
SP - 1306
EP - 1322
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 5
ER -
ID: 86663585