Geodesic
Approximation to the Function ~$z^{\alpha}$ by Rational Fractions in a Domain with Zero External Angle
Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 761-772

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Rational approximations to the function $z^{\alpha}$, $\alpha\in\mathbb{R}\setminus\mathbb{Z}$, were studied by Newman, Gonchar, Bulanov, Vyacheslavov, Andersson, Stahl, and others. The present paper deals with the order of best rational approximations to this function in a domain with zero external angle and vertex at the point $z=0$. In particular, the obtained results show that the conditions imposed on the boundary of the domain in the Jackson-type inequality proved by the author in 2001 for the best rational approximations in Smirnov spaces cannot be weakened significantly.
Keywords: best uniform rational approximation, Smirnov space, analytic function, rational function, rectifiable Jordan boundary
Mots-clés : polynomial approximation, Lavrentiev curve. 
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     author = {A. A. Pekarskii},
     title = {Approximation to the {Function} ~$z^{\alpha}$ by {Rational} {Fractions} in a {Domain} with {Zero} {External} {Angle}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {761--772},
     publisher = {mathdoc},
     volume = {91},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a11/}
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A. A. Pekarskii. Approximation to the Function ~$z^{\alpha}$ by Rational Fractions in a Domain with Zero External Angle. Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 761-772. http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a11/