Some extremal functions in Fourier analysis, III

Abstract

We obtain the best approximation in $L^1(\mathbb{R})$, 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.

26 pages. Submitted

References in corpus (1)

• Some extremal functions in Fourier analysis, II

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