Abstract
We obtain the best approximation in L 1(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.
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Communicated by Tim N.T. Goodman.
Research of the first author was supported by CAPES/FULBRIGHT grant BEX 1710-04-4. Research of the second author was supported by the National Science Foundation, DMS-06-03282.
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Carneiro, E., Vaaler, J.D. Some Extremal Functions in Fourier Analysis, III. Constr Approx 31, 259–288 (2010). https://doi.org/10.1007/s00365-009-9050-6
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DOI: https://doi.org/10.1007/s00365-009-9050-6