Recovery solutions of the Volterra equation of the first kind of convolution on the half with incomplete data

In this paper we study the integral equation Volterra first kind of convolution in the scalar and vector cases on the semi-infinite interval. Under the enough of the nature restrictions on the kernel of the integral equation of Volterra operator (the kernel has bounded support), the solution is restored by the right side of the equation, the latter is defined on the infinite part semi-infinite interval. Uniqueness theorems are proved, necessary and sufficient conditions for solvability are found, explicit formulas for solutions are received.