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 - Jurakhonov О.А. (Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, computer science, mechanics series, 2018)
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.