Geodesic
Approximation of functions by universal sums of series with respect to subsystems of Hermite polynomials
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2013), pp. 16-20

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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.
Keywords: uniform approximation, universal series, Hermite polynomials. 
@article{IVM_2013_9_a1,
     author = {L. K. Dodunova and O. V. Tyutyulina},
     title = {Approximation of functions by universal sums of series with respect to subsystems of {Hermite} polynomials},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {16--20},
     publisher = {mathdoc},
     number = {9},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_9_a1/}
}
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L. K. Dodunova; O. V. Tyutyulina. Approximation of functions by universal sums of series with respect to subsystems of Hermite polynomials. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2013), pp. 16-20. http://geodesic.mathdoc.fr/item/IVM_2013_9_a1/