Approximation of Periodic Functions of Many Variables by Functions of a Smaller Number of Variables in Orlicz Metric Spaces
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For periodic functions of many variables, we propose a method for their approximation in the Orlicz spaces L(𝕋m). According to this method, the functions are approximated by the sums of functions of smaller number of variables each of which is piecewise-constant in one variable for fixed values of the other variables. A Jackson-type inequality is analyzed for these approximations in terms of the mixed module of continuity.
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