On absolute convergence of Haar-Fourier series of superpositions of functions (Q1059810)

Several open problems are answered in this impressive paper about the absolute convergence of Fourier-Haar series of composed functions. Let us cite here only the following beautiful theorem: Let \(\phi\) be a real function on [a,b]. A necessary and sufficient condition that \(\phi\) \(\circ f\) have absolutely convergent Fourier-Haar series if f does so (f(t)\(\in [a,b]\), \(t\in [0,1])\) is that \(\phi\) be linear on [a,b].