On the method of two-sided continuation of solutions of the integral convolution equation on a finite Interval

The paper is devoted to the development of the method of two-sided continuation of the solution of the integral convolution equation with an even kernel function K ∈ L 1 (− r, r ). Two continuations of the solution S are considered: to (−∞, 0] and to [ r ,∞). A Wiener–Hopf-type factorization is used. Under invertibility conditions for some operators, the problem can be reduced to two equations with sum kernels: Applied aspects of the realization of the method are discussed.