On a generalization of the system of functions of Rademacher and Walsh

• Date: 2017
• Author Affiliations: М. В. Працьовитий — Нацiональний педагогiчний унiверситет iменi М. П. Драгоманова; Ю. П. Маслова — Нацiональний педагогiчний унiверситет iменi М. П. Драгоманова
• Keywords: keywords
• Main Authors: Pratsevity, M. V., Maslova, Yu. P., Працевитый, М. В., Маслова, Ю. П., Працьовитий, М. В.
• Format: Article
• Language: Ukrainian
• Published: Інститут математики НАН України 2017
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/49
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

In the paper, we propose generalizations of the Rademacher and Walsh functions. They are based on $????_2$-representation of real numbers generalizing classic binary representation of numbers $????\in[0;1]$. We study integral properties of these functions. In particular, we prove that generalized Ra...