An extremal problem with the Wiener-Hopf operator (Q5951156)

The author considers the following extremal problem \[ \int^\infty_{-\infty} e^{ax}\left|u(x)+\int^\infty_0 k(x-s)u(s)ds-g(x) \right|^2 dx\to\inf., \] where the unknown function \(u\in L^2(0,\infty)\) vanishes for \(x<0\), \(k\in L(-\infty, \infty)\), \(g\in L^2(-\infty, \infty)\), \(a\) are given. The problem is transformed into a Riemann boundary value problem on two parallel lines. A condition for the existence and uniqueness of a solution is given.