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On solvability of singular integral-differential equations with convolution
Pingrun Li
Keywords:singular integral-differential equations; Riemann boundary value problem; integral operators; Cauchy kernel; convolution type
Abstract:
      In this paper, we study a class of singular integral-different equations of convolution type with Cauchy kernels. By means of the classical boundary value theory, of the theory of Fourier analysis, and of the principle of analytic continuation, this class of equations are transformed into Riemann-Hilbert boundary value problems with discontinuous coefficients, and we obtain the general solutions and conditions of solvability in class $\{0\}$. Thus, the result in this paper generalizes the classical theory of integral equations and boundary value problems.