Integral equations on the half-line with difference kernels and nonlinear functional equatons

In this paper we present a new approach to the solution of scalar and operator equations of the form
\begin{equation*} f(x)=g(x)+\int_0^\infty T(x-t)f(t)\,dt. \tag{A} \end{equation*}

We derive and study some new functional equations, occupying an intermediate position between the equation (A) and the Ambarcumyan equation. This approach leads to a very simple way of deriving and generalizing Ambarcumyan's equations.
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