On a Wiener-Hopf integral equation (Q1914813)

The author considers the following problem: determine the positive sequence \(\{E_n\}\) satisfying the infinite discrete system \[ \sin \left( {\pi \over 4} + \theta \right) \sum_{n = 0}^\infty {E_n \over \beta_n - \theta} + \sin \left( {\pi \over 4} - \theta \right) \sum^\infty_{n = 0} {E_n \over \beta_n + \theta} = \sqrt 2 {\sin \theta \over \theta} \sum^\infty_{n = 0} {E_n \over \beta_n}, \] where \(\beta_n = (n + 3/4) \pi\). This system is connected with some Wiener-Hopf integral equation. With an additional assumption he also shows that \(\sum^\infty_{n = 0} {E_n \over \beta_n} = 1\).