Geodesic
Approximation of Classes of Periodic Functions in Several Variables
Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 109-121

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We study the approximation of the classes $B_{p,\theta }^r$ and $W_{p,\alpha }^r$ of periodic functions of several variables by multiple Fourier sums of fixed order constructed with regard to individual properties of functions from these classes. In a number of cases, such approximations allow us to achieve a better degree of approximation of the classes indicated above as compared to their approximation by staircase hyperbolic Fourier sums. 
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     author = {A. S. Romanyuk},
     title = {Approximation of {Classes} of {Periodic} {Functions} in {Several} {Variables}},
     journal = {Matemati\v{c}eskie zametki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a9/}
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A. S. Romanyuk. Approximation of Classes of Periodic Functions in Several Variables. Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 109-121. http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a9/