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Volume 9, Number 3, 2019, Pages 1071-1082                                                                DOI:10.11948/2156-907X.20180264
On solvability of singular integral-differential equations with convolution
Pingrun Li
Keywords:Singular integral-differential equations, Riemann-Hilbert problems; integral operators, Cauchy kernel, convolution type.
      In this paper, we study a class of singular integral-different equations of convolution type with Cauchy kernel. By means of the classical boundary value theory, of the theory of Fourier analysis, and of the principle of analytic continuation, we transform the equations into the Riemann-Hilbert problems with discontinuous coefficients and 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.
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