On the sets of divergence of multiple Fourier–Haar series

• Дата: 2023
• Автори: Bitsadze, K. R., Біцадзе, К. Р., Біцадзе, K. R.
• Формат: Стаття
• Мова: Українська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2023
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/6886
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.518.45 It is shown that every at most countable set $F$ in an $n$-dimensional unit cube $[0,1]^n$ is a set of divergence of the $n$-fold Fourier–Haar series of a certain limited dimensional function, i.e., there exists a bounded dimensional function defined on $[0,1]^n$ whose $n$-fold Fourie...