Sharp inequalities of Jackson type in weighted space $$$L_{2;\rho}({\mathbb{R}}^2)$$$

S.B. Vakarchuk; M.B. Vakarchuk

doi:10.15421/241403

Sharp inequalities of Jackson type in weighted space $L_{2;\rho}({\mathbb{R}}^2)$

S.B. Vakarchuk (Alfred Nobel Dnipropetrovsk University), https://orcid.org/0000-0002-2562-8844
M.B. Vakarchuk (Oles Honchar Dnipropetrovsk National University)

Abstract

Sharp inequalities of Jackson type, connected with the best approximation by "angles" of algebraic polynomials have been obtained on the classes of differentiable functions of two variables in the metric of space

$L_{2;\rho}({\mathbb{R}}^2)$ of the Chebyshev-Hermite weight.

Keywords

generalized modulus of continuity; best approximation by "angle"; Chebyshev-Hermite polynomials

Full Text:

PDF (Русский)

References

Abilov V.A., Abilov M.V. "Approximation of functions in $L_2({\mathbb{R}}^N;\exp(-|x|^2)$ ", Matem. zametki, 1995; 57(1): pp. 3-19. (in Russian) doi:10.1007/BF02309388

Szego G. Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ. vol. XXIII, Amer. Math. Soc, New York, 1959; Russian transl.: GIFML, Moscow, 1962.

Rzhavinskaya Ye.V. On approximation by algebraic polynomials in the metric of $L_p$ space with weight: Diss. cand. phys.-math. sc., Moscow, 1980; 126 p. (in Russian)

Potapov M.K. "On approximation by 'angle'", Proc. of the Conf. on Constructive Theory of Functions, Budapest, 1972; pp. 371-399. (in Russian)

Vakarchuk S.B. "On the best approximation by generalized polynomials in one space of analytical functions of two complex variables", Izv. vuzov. Matematika, 1991; 7: pp. 14-25. (in Russian)