Friedrich Littmann

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In this note we study the connection between best approximation and interpolation by entire functions on the real line. A general representation for entire interpolants is outlined. As an illustration, best upper and lower approximations from the class of functions of fixed exponential type to the Gaussian are constructed. §1. Approximation Background The(More)
Let f : R→ R have an nth derivative of finite variation Vf(n) and a locally absolutely continuous (n− 1)st derivative. Denote by E±(f, δ)p the error of onesided approximation of f (from above and below, respectively) by entire functions of exponential type δ > 0 in Lp(R)–norm. For 1 ≤ p ≤ ∞ we show the estimate E±(f, δ)p ≤ C n π1/pVf(n)δ −n− 1 p , with(More)
The zero sets of (D + a)g(t) with D = d/dt in the (t, a)plane are investigated for g(t) = te(e−1) and g(t) = e(e+1). The results are used to determine entire interpolations to functions xn+e , which give representations for the best approximation and best one-sided approximation from the class of functions of exponential type η > 0 to xn+e .
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