Solving convolution singular integral equations with reflection and translation shifts utilizing Riemann-Hilbert approach. (English) Zbl 07885960
Summary: In this paper, method of solution for some kinds of convolution singular integral equations with reflection will be discussed in class {0}. By means of the theory of Fourier analysis and the theory of boundary value problems of analytic functions, such equations can be transformed into Riemann boundary value problems (i.e., Riemann-Hilbert problems) with nodes and reflection, or a system of linear algebraic equations. In spite of the classical method for solution, we are to give a new method, by which analytic solutions and conditions of Noether solvability are obtained respectively. At the end of this paper, we propose two kinds of convolution singular integral equations with reflections and a finite set of translation shifts.
MSC:
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 45E05 | Integral equations with kernels of Cauchy type |
| 30E25 | Boundary value problems in the complex plane |
Keywords:
singular integral equations of convolution type; Riemann-Hilbert problems; Noether theory; reflection; translation shiftsReferences:
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