Finkelstein, Mark; Whitley, Robert Eigenvalues, almost periodic functions, and the derivative of an integral. (English) Zbl 1126.26010 Am. Math. Mon. 112, No. 7, 639-641 (2005). The authors prove that if a function \(g\) is nonconstant and almost periodic on \(\mathbb R\), then the limit \(\lim_{z\to \infty}\int_0^{\infty}g(y+z)e^{-y}\,dy\) does not exist. Using this result they show that every nonconstant almost periodic function \(g\) has the property that \(G(x)=\int_0^xg(-\log t)\,dt\) is not differentiable from the right at \(0\). Reviewer: Silvia-Otilia Corduneanu (Iaşi) MSC: 26A36 Antidifferentiation 26A46 Absolutely continuous real functions in one variable 42A75 Classical almost periodic functions, mean periodic functions Keywords:eigenvalue; almost periodic function PDFBibTeX XMLCite \textit{M. Finkelstein} and \textit{R. Whitley}, Am. Math. Mon. 112, No. 7, 639--641 (2005; Zbl 1126.26010) Full Text: DOI Link