Geodesic
On representation of piecewise-smooth functions by rapidly convergent trigonometric series
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 4, pp. 385-394 
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/
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     title = {On representation of piecewise-smooth functions by rapidly convergent trigonometric series},
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     url = {http://geodesic.mathdoc.fr/item/SJVM_1999_2_4_a7/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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[2] Smelov V. V., “K voprosu ob approksimatsii funktsii sobstvennymi resheniyami dvukh zadach Shturma–Liuvillya”, Sibirskii matematicheskii zhurnal, 26:2 (1985), 149–158 | MR | Zbl

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[4] Nikolskii S. M., Kurs matematicheskogo analiza, Nauka, M., 1983

[5] Mikhlin S. G., Variatsionnye metody v matematicheskoi fizike, Nauka, M., 1970 | MR | Zbl

[6] Smelov V. V., Plekhanova E. I., Approksimatsiya kusochno-gladkikh funktsii sobstvennymi resheniyami zadach Shturma–Liuvillya (teoriya i illyustratsiya), Preprint / AN SSSR. Sib. Otd-nie VTs; 679, Novosibirsk, 1986 | MR | Zbl