Geodesic
Optimal subspaces for mean square approximation of classes of differentiable functions on the half-line
Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part III, Tome 539 (2024), pp. 44-65 
O. L. Vinogradov; A. Yu. Ulitskaya. Optimal subspaces for mean square approximation of classes of differentiable functions on the half-line. Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part III, Tome 539 (2024), pp. 44-65. http://geodesic.mathdoc.fr/item/ZNSL_2024_539_a2/
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     title = {Optimal subspaces for mean square approximation of classes of differentiable functions on the half-line},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We obtain sharp inequalities for the best mean square approximation of two classes of functions on the half-line, defined by boundary conditions corresponding to even and odd extension of a function. Optimal subspaces are provided by even and odd parts of the spaces generated by equidistant shifts of a single function. Under certain additional conditions on this function, the sharpness of the inequalities in the sense of average widths is proved.

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