Convergence Almost Everywhere of Orthorecursive Expansions in Systems of Translates and Dilates

Авторы: Galatenko Vladimir V., Lukashenko Taras P., Sadovnichiy Victor A.
Сборник: Modern Mathematics and Mechanics
Серия: Understanding Complex Systems
Год издания: 2019
Место издания: Springer
Первая страница: 3
Последняя страница: 11
DOI: 10.1007/978-3-319-96755-4_1
Аннотация: Systems of translates and dilates have been widely studied in the last decades. In particular, V.I. Filippov and P. Oswald obtained conditions on a generating function which guarantee that dyadic translates and dilates of this function form a representation system in L^p[0, 1]. A.Yu. Kudryavtsev and A.V. Politov showed that under a slightly harder condition on a generating function each element f ∈ L^2[0, 1] is represented by its orthorecursive expansion in this system. Here we continue studying orthorecursive expansions in systems of dyadic translates and dilates and present results on convergence almost everywhere of these expansions.
Добавил в систему: Галатенко Владимир Владимирович

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