5 research outputs found
ONE-SIDED -APPROXIMATION ON A SPHERE OF THE CHARACTERISTIC FUNCTION OF A LAYER
In the space of functions integrable on the unit sphere of the Euclidean space of dimension , we discuss the problem of one-sided approximation to the characteristic function of a spherical layer where is one of the intervals and by the set of algebraic polynomials of given degree in variables. This problem reduces to the one-dimensional problem of one-sided approximation in the space with the ultraspherical weight to the characteristic function of the interval . This result gives a solution of the problem of one-sided approximation to the characteristic function of a spherical layer in all cases when a solution of the corresponding one-dimensional problem known. In the present paper, we use results by A.G.Babenko, M.V.Deikalova, and Sz.G.Revesz (2015) and M.V.Deikalova and A.Yu.Torgashova (2018) on the one-sided approximation to the characteristic functions of intervals