On $\mathbb R$-linear problem and truncated Wiener–Hopf equation

We consider the $\mathbb R$-linear problem (also known as the Markushevich problem and the generalized Riemann boundary value problem) and the convolution integral equation of the second kind on a finite interval (also known as the truncated Wiener–Hopf equation). We find new conditions for correct solvability of the $\mathbb R$-linear problem and the truncated Wiener–Hopf equation.