Найкращі наближення класів періодичних функцій багатьох змінних з обмеженою домінуючою мішаною похідною
Анотація
УДК 517.51
Встановлено точні за порядком оцінки наближення класів Соболєва $W^{\boldsymbol{r}}_{p,\boldsymbol{\alpha}}(\mathbb{T}^d)$ періодичних функцій багатьох змінних з обмеженою домінуючою мішаною похідною. Наближення здійснюється за допомогою тригонометричних поліномів зі спектром у східчастих гіперболічних хрестах, а похибка оцінюється в метриці простору $B_{q,1}(\mathbb{T}^d),$ $1 \leq p, q < \infty.$
Посилання
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