The author studies \(g\)-additive and \(g\)-multiplicative functions where \(g\geq 2\) is a basis of the \(g\)-representation of nonnegative integers. He finds criteria for these functions to belong to the class of uniformly or limit almost-periodic functions. He also gives conditions for when such functions can be approximated by linear combinations of exponential functions \(\exp\{2\pi i\alpha n\}\), \(\alpha\in\mathbb R\), in the semi-norm \[ \| f\| :=\bigg(\limsup_ {N\to\infty}\frac1N\sum_ {n=0}^ {\infty} | f(n)| ^ q\bigg)^ {1/q},\quad q\geq1, \] or, equivalently, for when they belong to the classes \(\mathcal A^ q\) or \(\mathcal D^ q\) defined in the book of W. Schwarz and the author [Arithmetical functions. Cambridge: Cambridge University Press (1994; Zbl 0807.11001)]. Some of the results were given in the paper by M. Peter and the author [Manuscr. Math. 105, No. 4, 519–536 (2001; Zbl 1016.11029)].
For the entire collection see [Zbl 1006.00014].