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Upper Bounds for the Approximation of Some Classes of Bivariate Functions by Triangular Fourier-Hermite Sums in the Space L2,ρ(ℝ2)

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Abstract

We evaluate the suprema of approximations of bivariate functions by triangular partial sums of the double Fourier-Hermite series on the class of functions Lr2(D) in the space L2,ρ(ℝ2), where D is the second-order Hermite operator. Sharp Jackson-Stechkin type inequalities on the sets L2,ρ(ℝ2) are obtained, in which the best approximation is estimated from above both in terms of moduli of continuity of order m and in terms of K-functionals. N-widths of some classes of functions in L2,ρ(ℝ2) are evaluated.

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Authors and Affiliations

  1. Tajik National University, Rudaki Ave. 17, 734025, Dushanbe, Tajikistan

    M. Sh. Shabozov & O. A. Dzhurakhonov

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  1. M. Sh. Shabozov
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  2. O. A. Dzhurakhonov
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Correspondence to M. Sh. Shabozov.

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Shabozov, M.S., Dzhurakhonov, O.A. Upper Bounds for the Approximation of Some Classes of Bivariate Functions by Triangular Fourier-Hermite Sums in the Space L2,ρ(ℝ2). Anal Math 45, 823–840 (2019). https://doi.org/10.1007/s10476-019-0010-5

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  • DOI: https://doi.org/10.1007/s10476-019-0010-5

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