Geodesic
Sharp estimates of best approximations by deviations of Weierstrass-type integrals
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 40, Tome 401 (2012), pp. 53-70

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We establish the estimates $$ A_\sigma(f)_P\le KP(f-f*W), $$ where $W$ is a kernel of special type summable on $\mathbb R$ and $A_\sigma(f)_P$ is the best approximation (with respect to a seminorm $P$) of a function $f$ by entire functions of exponential type not greater than $\sigma$. For the uniform and the integral norm we find the least possible constant $K$. The estimates are obtained by linear methods of approximation. 
@article{ZNSL_2012_401_a1,
     author = {O. L. Vinogradov},
     title = {Sharp estimates of best approximations by deviations of {Weierstrass-type} integrals},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {53--70},
     publisher = {mathdoc},
     volume = {401},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_401_a1/}
}
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O. L. Vinogradov. Sharp estimates of best approximations by deviations of Weierstrass-type integrals. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 40, Tome 401 (2012), pp. 53-70. http://geodesic.mathdoc.fr/item/ZNSL_2012_401_a1/