The inverse and direct problem for equation of the first kind of convolution on the half-line

摘要

In this paper we study the integral equation first kind ofconvolution on the semi-infinite interval. The next two tasks are:1. Task is reconstruction of history. From the integral equation it isrequired to find two functions u(t) for t>0 and f(t) for 0b (u(t) — solution ofintegral equation).2. The problem of inversion of the integral operator.Uniqueness theorems are proved, necessary and sufficient conditions forsolvability are found, explicit formulas for solutions are received.