Kubaturnye Formuly S Pogranichnym Sloem

Zadacha o postroenii formul dlya priblizhennogo vychisleniya integralov yavlyaetsya odnoy iz klassicheskikh zadach vychislitel'noy matematiki. Shirokoe primenenie metodov funktsional'nogo analiza i teorii differentsial'nykh uravneniy v issledovaniyakh po teorii priblizhennogo integrirovaniya nachalos' rabotami S.M. Nikol'skogo i S.L. Soboleva. V dal'neyshem eti metody byli razvity v rabotakh V. I. Polovinkina, M.D. Ramazanova, Ts.B. Shoynzhurova, V.L. Vaskevicha i drugikh avtorov. V nastoyashchey rabote rassmatrivayutsya vesovye formuly v prostranstvakh W_^m (E_n), kak predel'nogo sluchaya ranee issledovannykh prostranstv. Krome togo, M.D. Ramazanovym provodilis' issledovaniya kubaturnykh formul dlya oblastey s gladkimi granitsami. V dannoy rabote, opirayas' na metodiku Ramazanova, polucheny formuly s pogranichnym sloem, v kotorykh koeffitsienty vychislyayutsya znachitel'no proshche.