Geodesic
On representation of piecewise-smooth functions by rapidly convergent trigonometric series
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 4, pp. 385-394

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A specific variant of expansions of smooth and piecewise-smooth functions to rapidly convergent series with respect to trigonometric functions is suggested. This result is the basis for the effective approximations of the above-mentioned functions. 
@article{SJVM_1999_2_4_a7,
     author = {V. V. Smelov},
     title = {On representation of piecewise-smooth functions by rapidly convergent trigonometric series},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {385--394},
     publisher = {mathdoc},
     volume = {2},
     number = {4},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1999_2_4_a7/}
}
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V. V. Smelov. On representation of piecewise-smooth functions by rapidly convergent trigonometric series. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 4, pp. 385-394. http://geodesic.mathdoc.fr/item/SJVM_1999_2_4_a7/