Singular modifications of a classical function. (English) Zbl 07829366
Summary: The present article deals with properties of one class of functions with complicated local structure. These functions can be modeled by certain operators of digits. Such operators were considered by the author earlier. This research is a generalization of investigations presented in the last-mentioned papers.
MSC:
| 11K55 | Metric theory of other algorithms and expansions; measure and Hausdorff dimension |
| 11J72 | Irrationality; linear independence over a field |
| 26A27 | Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives |
| 11B34 | Representation functions |
| 39B22 | Functional equations for real functions |
| 39B72 | Systems of functional equations and inequalities |
| 26A30 | Singular functions, Cantor functions, functions with other special properties |
| 11B34 | Representation functions |
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