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Characteristic functions and products of bounded derivatives. (English) Zbl 0833.26008

The author shows which characteristic functions can be expressed as the product of two or more bounded derivatives. The main result of the paper asserts: Let \(S \subset R\) \((R\) – the real line) be ambiguous (i.e., both an \(F_\sigma\) and a \(G_\delta\) set) and \(T = R - S\) be nonporous. Then there exist derivatives \(f,g\): \(R \to R\) such that (i) \(f\cdot g = 0\) on \(T\); (ii) \(f = g\) and \(|f |= 1\) on \(S\); (iii) \(|f |< 2\), \(|g |< 2\).

MSC:

26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
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