NOETHERIAN SOLVABILITY FOR CONVOLUTION SINGULAR INTEGRAL EQUATIONS WITH FINITE TRANSLATIONS IN THE CASE OF NORMAL TYPE

In this paper, we mainly study the solvability for some classes of convolution singular integral equations with finite translations in the case of normal type. Via using Fourier transforms, we transform these equations into Riemann boundary value problems with nodes. By means of the classical theory of Riemann-Hilbert problems and the principle of analytic continuation, we discuss the general solutions and conditions of solvability in the normal type. Due to the coefficients of Riemann boundary value problems contain discontinuous points, thus we discuss the solvable conditions and the properties for the equation near the nodes. Unlike the general convolution equations, the unknown function in the questions has finite translations on the real axis, so it is a further generalization of the classical theory of singular integral equations.