On Approximation by Entire Functions on an Unbounded Quasi-Smooth Curve

Kurzfassung/Abstract

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 → ∞.