The solvability and properties of solutions of an integral convolutional equation

The work defines the conditions of solvability of one integral convolutional equation with degreely difference kernels. This type of integral convolutional equations was not studied earlier, and it turned out that all methods used for the investigation of such equations with the help of Riemann boundary problem at the real axis are not applied there. The investigation of such type equations is based on the investigation of the equivalent singular integral equation with the Cauchy type kernel at the real axis. It is determined that the equation is not a Noetherian one. Besides, there shown the number of the linear independent solutions of the homogeneous equation and the number of conditions of solvability for the heterogeneous equation. The general form of these conditions is also shown and there determined the spaces of solutions of that equation. Thus the convolutional equation that wasn't studied earlier is presented at that work and the theory of its solvability is built there. So some new and interesting theoretical results are got at that paper.