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Convergence Almost Everywhere of Orthorecursive Expansions in Functional Systemsстатья
- Авторы: Galatenko Vladimir V., Lukashenko Taras P., Sadovnichiy Victor A.
- Сборник: Advances in Dynamical Systems and Control
- Редактор: Садовничий Виктор Антонович
- Серия: Studies in Systems, Decision and Control
- Том: 69
- Глава в коллективной монографии
- Год издания: 2016
- Место издания: Springer Switzerland
- Первая страница: 3
- Последняя страница: 11
- DOI: 10.1007/978-3-319-40673-2_1
- Аннотация: Along with the convergence in L2-norm, convergence almost everywhere of expansions in functional systems is a property of interest for both theoretical studies and applications. In this paper we present results on convergence almost everywhere for orthorecursive expansions which are a natural generalization of classical expansions in orthogonal systems. As a corollary of a more general result, we obtain a condition on coefficients of an expansion that guarantees convergence almost everywhere. We also show that this condition cannot be relaxed.
- Добавил в систему: Галатенко Владимир Владимирович