Some Extremal Functions in Fourier Analysis, III
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- Carneiro, E. & Vaaler, J.D. Constr Approx (2010) 31: 259. doi:10.1007/s00365-009-9050-6
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We obtain the best approximation in L1(ℝ), by entire functions of exponential type, for a class of even functions that includes e−λ|x|, where λ>0, log |x| and |x|α, where −1<α<1. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded degree.