A class of linear integral equations and systems with sum and difference kernel (Q1431147)

In the space \(L^2(0,T), 0<T\leq\infty\) the author considers a linear integral equation with sum and difference kernels of the form \[ p(t)-\int_{0}^{T-t} \overline{k(s)}p(s+t)\,ds- \int_{0}^{T-t}k(s+t) \overline{p(s)}\,ds= g(t), \quad 0<t<T. \] Under the assumption that \(k(t)\in L^1(0,T)\) the solution of this equation is constructed in the regular and the singular case. Systems of these equations and the first kind analog are also discussed.