Abstract
The uniform approximation of functions from a certain class on compact sets was performed first by means of polynomials, then by partial sums of universal functional series, and further by special sums associated with functional series. In this paper we construct universal sums associated with Hermite polynomials (any function from this class on compact sets is approximated by these sums). We apply the matrix transformation method that was used earlier for constructing special sums for other functional series.
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Original Russian Text © L.K. Dodunova and O.V. Tyutyulina, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 9, pp. 16–20.
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Dodunova, L.K., Tyutyulina, O.V. Approximation of functions by universal sums of series in subsystems of hermite polynomials. Russ Math. 57, 12–15 (2013). https://doi.org/10.3103/S1066369X13090028
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DOI: https://doi.org/10.3103/S1066369X13090028