Abstract
We consider some system of polynomials orthonormal with respect to the Sobolev-type inner product and generated by the classical Laguerre polynomials. Earlier, the approximation properties of the partial sums of Fourier series in this system have already been studied. Under study is the approximation of functions from a Sobolev space by the Vallée-Poussin means of the partial sums of Fourier series in the above system. We show that the Vallée-Poussin means converge to functions from the Sobolev space at the rate of the best deviation.
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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 3, pp. 545–561. https://doi.org/10.33048/smzh.2022.63.306
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Gadzhimirzaev, R.M. Approximation Properties of the Vallée-Poussin Means Similar to the Partial Sums of Fourier Series in Laguerre–Sobolev Polynomials. Sib Math J 63, 451–465 (2022). https://doi.org/10.1134/S0037446622030065
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DOI: https://doi.org/10.1134/S0037446622030065