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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:Systems of dyadic wavelets on the positive half-line R_+ equipped with the operation of binary summation are studied. Several problems concerning approximation properties of such wavelets are solved. In particular, explicit formulas for the order of approximation of smooth functions and of binary-smooth functions on R_+ (smooth in the dyadic metric on the binary half-line) are obtained. The dyadic approximations with best approximation properties are characterized. The relation between the smoothness of wavelets and their order of approximation is analyzed in various function spaces.