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

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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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     author = {K.Tukhliev and A. M. Tuichiev},
     title = {Mean-square approximation of functions on the whole axis by algebraic polynomials with the {Chebyshev-Hermite} weight},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {270--277},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2020_26_2_a20/}
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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/