Approximation of Periodic Functions of Many Variables by Functions of a Smaller Number of Variables in Orlicz Metric Spaces

Babich, Yu. A.Mikhailova, T. F.2020-01-222020-01-222019Babich Y. A., Mikhailova T. F. Approximation of Periodic Functions of Many Variables by Functions of a Smaller Number of Variables in Orlicz Metric Spaces. Ukrainian Mathematical Journal. 2019. Vol. 70. Iss. 8. P. 1319–1325. DOI: 10.1007/s11253-018-1571-3. (Ukrainian Original Vol. 70, No. 8, August, 2018).http://eadnurt.diit.edu.ua/jspui/handle/123456789/11772https://link.springer.com/journal/11253/70/8https://link.springer.com/content/pdf/10.1007%2Fs11253-018-1571-3.pdfEN: For periodic functions of many variables, we propose a method for their approximation in the Orlicz spaces Lφ (T^m). 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.enapproximationrecurrent functionsvariablesmetric spacesКПМApproximation of Periodic Functions of Many Variables by Functions of a Smaller Number of Variables in Orlicz Metric SpacesArticle