On the sets of divergence of multiple Fourier–Haar series

• Date: 2023
• Main Authors: Bitsadze, K. R., Біцадзе, К. Р., Біцадзе, K. R.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2023
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/6886
• Journal Title: 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...