Convolution equations on the half-line with symbols degenerating on an interval (Q5930627)

The author consider first- and second-kind convolution equations in \(L_2 (0,\infty)\) with a kernel from \(L_1({\mathbf R})\) and with degenerating symbols on an interval. Uniqueness theorems and necessary and sufficient existence conditions are established. It is shown that the respective solutions can be represented through Carleman type formulas. As an intermediate result, Carleman formulas for the solutions of the Riemann boundary value problem on \({\mathbf R}\) with coefficient degenerating on the interval \((a,b)\) are obtained.