The quasi-periodic Riemann boundary-value problem with a variable coefficient (Q2276617)

Let \(\mathbf L_0:=(a_0,1), a_0>0, {\mathbf L}_k:= {\mathbf L}_0+k, k \in \mathbb R\) and let \(\mathbf L : =\bigcup_{k=0} {\mathbf L}_{k}\). The authors investigate the Riemann boundary value problem \(\Phi^{+}= G\Phi^{-}+ g\) on \(\mathbf L\) where the given functions \(G, g\) satisfy the Hölder condition, \(G(t+1)=G(t), t \in {\mathbf L}\). In this paper, solutions of the problem are sought for in three different classes of functions.