Computational Methods and Function Theory 9 (2009), No. 2, 525--550
Copyright Heldermann Verlag 2009
On Approximation by Entire Functions on an Unbounded Quasi-Smooth Curve
Vladimir V. Andrievskii
email@example.com , Kent State University, Department of Mathematical Sciences, Kent, OH 44242, U.S.A.
firstname.lastname@example.org , Katholische Universität Eichstätt-Ingolstadt, Ostenstrasse 26-28, 85072 Eichstätt, Germany.
We generalize a classical Bernstein Theorem about approximation of functions on the real line by entire functions of the exponential type, i.e. for any function f continuous and bounded on an unbounded quasi-smooth (in the sense of Lavrentiev) curve L in the complex plane we construct entire functions of exponential type σ>0 which in some sense converge optimally to f on L as σ→∞.
Keywords: Entire functions of exponential type, approximation, continuous function, quasiconformal mapping, quasi-smooth curve.
MSC 2000: 30C10, 30E10.
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