Some extremal functions in Fourier analysis, III

Details Some extremal functions in Fourier analysis, III Some extremal functions in Fourier analysis, III

2008-09-23

arxiv.org/abs/0809.4053v1

Constructive Approximation, v. 31, p. 259-288, 2010

Mathematics

Classical Analysis and ODEs

26 pages. Submitted

Scientific paper

10.1007/s00365-009-9050-6

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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