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arXiv · 0809.4053

Some extremal functions in Fourier analysis, III

Emanuel Carneiro·Jeffrey D. Vaaler
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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 $e^{-\lambda|x|}$, where $\lambda >0$, $\log |x|$ and $|x|^{\alpha}$, where $-1 < \alpha < 1$. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded degree.

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Emanuel Carneiro, Jeffrey D. Vaaler. 2008-09-23. Some extremal functions in Fourier analysis, III. https://doi.org/10.1007/s00365-009-9050-6

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