Singularities of the Weierstrass type functions (Q1114030)

Let q(x) be a real-valued almost periodic function, and let \(f(x)=\sum^{\infty}_{n=0}\lambda^ nq(\beta^ nx),\quad 0<\lambda <1.\) The author considers, assuming \(\lambda \beta >1,\) such differentiability properties of f as the uniform \(\Omega\)-property of the difference \(f(x+h)-f(x),\) the problem of knot points, and finally, for \(q(x)=\cos x\) and \(\lambda \beta \geq 1+\pi^ 2,\) he proves that f has no infinite or finite derivative at each point x.