On certain generalizations of one function and related problems (Systems of functional equations and generalizations of certain functions)

Abstract

The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of various representations of real numbers) include the generalized Salem functions and generalizations of the Gauss-Kuzmin problem.

arXiv comment14 pages. The present investigations were presented by the author in the preprint arXiv:1909.03163 in 2019

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• One modification of the Salem function
• One class of functions with arguments in negative bases
• On one approach to modeling numeral systems
• On one class of modifications of the Salem function
• On one map between singular expansions
• The Engel--Minkowski question-mark function
• A note on rational numbers and certain operators