О.А. Jurakhonov The exact values of the upper bounds for approximation in the mean of some classes of Ьivariate functions bу triangular Fourier-Hermite sums

Abstract

We evaluate the suprema of approximation of Ьivariate functions Ьу triangular partial sums of the douЫe Fourier-Hermite series on the class of functions L2(D) in the space L2,p(JR2 ), where D is the
second-order Hermite operator. Sharp Jackson-Stechkin type inequalities on the sets L2,p(JR2) are obtained, in which the best approximation is estimated from above both in terms of moduli of continuity of order m . N -widths of some classes of functions in L2,p(JR2 ) are evaluated.