Geodesic
Mean-square approximation of functions on the whole axis by algebraic polynomials with the Chebyshev-Hermite weight
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 26 (2020) no. 2, pp. 270-277 Cet article a éte moissonné depuis la source Math-Net.Ru

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We derive exact inequalities of Jackson–Stechkin type between the value $E_{n-1}(f^{(s)})_{2}$ of the best mean-square approximation on $\mathbb{R}$ with the weight $\rho(x)=e^{-x^2}$ of successive derivatives $f^{(s)}$, $s=0,1,...,r$, of functions $f\in L_{2,\rho}^{(r)}(\mathbb{R})$ and average values of $m$th-order generalized moduli of continuity of the $r$th derivatives. The exact values of some extremal approximation characteristics in the space $L_{2,\rho}(\mathbb{R})$ are found for classes of functions defined in terms of these moduli of continuity.
Keywords: best approximations, Jackson–Stechkin inequalities, $m$th-order modulus of continuity, Chebyshev–Hermite polynomial.
Mots-clés : algebraic polynomial 
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K.Tukhliev; A. M. Tuichiev. Mean-square approximation of functions on the whole axis by algebraic polynomials with the Chebyshev-Hermite weight. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 26 (2020) no. 2, pp. 270-277. http://geodesic.mathdoc.fr/item/TIMM_2020_26_2_a20/

[1] Rafalson S.Z., “O priblizhenii funktsii v srednem summami Fure — Ermita”, Izv. vuzov. Matematika, 1968, 78–84 | Zbl

[2] Suetin P.K., Klassicheskie ortogonalnye mnogochleny, Nauka, M., 1979, 416 pp.

[3] Abilov V.A., Abilova F.V., “Nekotorye voprosy priblizheniya funktsii summami Fure — Ermita v prostranstve $L_{2}(R;e^{-x^2})$”, Izv. vuzov. Matematika, 2006, 3–12 | Zbl

[4] Vakarchuk S.B. Vakarchuk M.B., “O priblizhenii funktsii algebraicheskimi polinomami v srednem na veschestvennoi osi s vesom Chebysheva — Ermita”, Visnik Dnipropetrovskogo universitetu. Seriya matematika, 19 (6/1) (2011), 28–31

[5] Vakarchuk S.B., Shvachko A.V., “O nailuchshem priblizhenii v srednem s vesom Chebysheva — Ermita algebraicheskimi polinomami na vsei veschestvennoi osi”, Zbirnik prats Institutu matematiki NAN Ukraini, 10 (2013), 28–38 | Zbl

[6] Vakarchuk S.B., “Priblizhenie funktsii v srednem na veschestvennoi osi algebraicheskimi polinomami s vesom Chebysheva — Ermita i poperechniki funktsionalnykh klassov”, Matem. zametki, 95 (2014), 666–684 | DOI | Zbl