Geodesic
Weight optimal cubature formulas in Sobolev's periodic space
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 2, pp. 185-196 
Kh. M. Shadimetov. Weight optimal cubature formulas in Sobolev's periodic space. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 2, pp. 185-196. http://geodesic.mathdoc.fr/item/SJVM_1999_2_2_a6/
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     author = {Kh. M. Shadimetov},
     title = {Weight optimal cubature formulas in {Sobolev's} periodic space},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {185--196},
     year = {1999},
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     url = {http://geodesic.mathdoc.fr/item/SJVM_1999_2_2_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the present paper the weight lattice optimal cubature formulas in the periodic Sobolev's space $\widetilde L_2^{(m)}(\Omega)$ are constructed. Under writing out of the algorithm of the construction the extremal function is found, and by means of the function the norm of the error functional of the cubature formula is calculated. Minimizing the norms, periodic Winier–Hopf's systems are obtained. Then the uniqueness solution to the system has been proved.

[1] Sobolev S. L., Vvedenie v teoriyu kubaturnykh formul, Nauka, M., 1974 | MR

[2] Sobolev S. L., Vaskevich V. L., Kubaturnye formuly, Izd-vo IM SO RAN, Novosibirsk, 1996 | Zbl

[3] Ramazanov M. D., “Ob optimalnykh funktsionalakh oshibki nad periodicheskimi funktsiyami iz banakhovykh prostranstv”, Sib. mat. zhurn., 13:2 (1972), 481–494 | MR

[4] Ramazanov M. D., “Optimalnyi funktsional oshibki nad periodicheskimi funktsiyami iz prostranstv $\widetilde H_p^\mu$”, Sib. mat. zhurn., 13:1 (1972), 225–229 | MR | Zbl

[5] Ramazanov M. D., “Universalnaya optimalnost reshetchatykh kubaturnykh formul”, Dokl. RAN, 324:5 (1992), 933–937 | MR | Zbl

[6] Polovinkin V. I., “Vesovye kubaturnye formuly v periodicheskom sluchae”, Mat. zametki, 179:3 (1968), 317–322 | MR

[7] Polovinkin V. I., “Vesovye kubaturnye formuly”, Dokl. AN SSSR, 179:3 (1968), 542–544 | MR | Zbl

[8] Babushka I., Vitasek E., Prager M., Chislennye protsessy resheniya differentsialnykh uravnenii, Mir, M., 1969 | MR