Truncated Wiener-Hopf equation and matrix function factorization (Q2200998)

The author considers the following convolution equation of second kind \(u(t)-\int_0^\tau k(t-s)u(s)ds=f(t)\) on the interval \((0,\tau),\,\tau>0\), where \(k\in L_1(-\tau,\tau)\) and \(f\in L_1(0,\tau)\). A connection of this equation and the Riemann-Hilbert boundary value problem in the Wiener algebra, whose matrix coefficient, denoted by \(G_\beta(x)\), parametrically depends on two functions \(\beta^\pm(x)\), and admits a standard factorization, is looked for.