Наближення сумами Фур’є на класах диференційовних у сенсі Вейля – Надя функцій із високим показником гладкості

А. С. Сердюк; І. В.  Соколенко

doi:10.37863/umzh.v74i5.7136

А. С. Сердюк Iн-т математики НАН України, Київ
І. В. Соколенко Iн-т математики НАН України, Київ

DOI: https://doi.org/10.37863/umzh.v74i5.7136

Ключові слова: Суми Фур'є,, клас Вейля-Надя, асимптотична рівність

Анотація

УДК 517.5

Встановлено асимптотичні оцінки точних верхніх меж відхилень у рівномірній метриці частинних сум Фур'є порядку $n-1$ на класах $2\pi$-періодичних функцій, диференційовних у сенсі Вейля–Надя, $W^r_{\beta,p}, 1\le p\le \infty, \beta\in\mathbb{R},$ при високих показниках гладкості $r\ (r-1\ge \sqrt{n}).$ Аналогічні оцінки встановлено і в метриках просторів $L_p, 1\le p\le\infty,$ для функціональних класів $W^r_{\beta,1}.$

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