The solvability of some kinds of singular integral equations of convolution type with variable integral limits. (English) Zbl 07924046
Summary: In this paper, we discuss several classes of convolution type singular integral equations with variable integral limits in class \(H^*_1 \). By means of the theory of complex analysis, Fourier analysis and integral transforms, we can transform singular integral equations with variable integral limits into the Riemann boundary value problems with discontinuous coefficients. Under the solvability conditions, the existence and uniqueness of the general solutions can be obtained. Further, we analyze the asymptotic properties of the solutions at the nodes. Our work improves the Noether theory of singular integral equations and boundary value problems, and develops the knowledge architecture of complex analysis.
MSC:
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 30E25 | Boundary value problems in the complex plane |
| 45E05 | Integral equations with kernels of Cauchy type |
Keywords:
singular integral equations; variable integral limits; Riemann boundary value problems; Wiener-Hopf type; dual type; Fourier integral transformReferences:
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