Singular Integral Equations of Convolution Type With Carleman Shift

This article discusses a few different types of singular integral equations of the convolution type with Carleman shift in class {0}. By using the theory of Fourier analysis, these equations under consideration are transformed into Riemann–Hilbert boundary value problems for analytic functions with shift and discontinuous coefficients. For such problems, we propose a method different from the classical ones, and we obtain the analytic solutions and the conditions of Noether solvability. MSC2010 Classification: 45E10, 45E05, 30E25