Approximation by Faber-Laurent Rational Functions on Doubly Connected Domains

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New Zealand Journal of Mathematics

Vol. 44, (2014), Pages 113-124


Hasan Yurt

Department of Mathematics,

Faculty of Arts and Sciences,

Canakkale Onsekiz Mart University,

17020 Canakkale, Turkey.

mailto:hyurt@comu.edu.tr

Ali Guven

Department of Mathematics,

Faculty of Arts and Sciences,

Balikesir University,

10145 Balikesir, Turkey.

mailto:guvennali@gmail.com




Abstract Let B be a doubly-connected domain bounded by two Dini-smooth curves. In this work, we prove some direct theorems of approximation theory in weighted rearrangement invariant Smirnov spaces E_{X}\left( B,\omega \right) defined on B. For this, approximation properties of the Faber-Laurent rational series expansions are used.

Keywords Cauchy singular operator, Faber-Laurent rational function, Muckenhoupt weight, weighted rearrangement invariant space.

Classification (MSC2000) 30E10, 41A20, 41A25, 46E30.

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