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Some Extremal Functions in Fourier Analysis, III

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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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Correspondence to Emanuel Carneiro.

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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

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