Some extremal functions in Fourier analysis, III

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.

No reviews yet.

No comments yet.