On a Pair Integral Equation and its Transpose

Abstract

In the present paper we study an integral equation of the form

$$\begin{matrix}\phi (\mathrm{t})-\int_{-\infty }^{\infty }\mathrm{k_1(t-s)}\phi \mathrm{(s)ds=f(t)}(-\infty <\mathrm{t}<0),\\ \phi (\mathrm{t})-\int_{-\infty }^{\infty }\mathrm{k_2(t-s)}\phi \mathrm{(s)ds=f(t)}(0 <\mathrm{t}<\infty ),\end{matrix}$$

((!))

where k₁(t) and k₂(t) are arbitrary functions belonging to the space L = L₁(−∞, ∞).

Translation of Teoreticheskaya i Prikladnaya Matematika, No. 1 (1958), 58-81.