Some extremal functions in Fourier analysis, III

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Carneiro, Emanuel
Vaaler, Jeffrey D.
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Abstract
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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.
Comment: 26 pages. Submitted
Keywords
Mathematics - Classical Analysis and ODEs, Mathematics - Complex Variables, 41A30, 41A52, 42A05
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