| The solvability of some kinds of singular integral equations of convolution type with variable integral limits |
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| 引用本文： | Pingrun Li,Wenwen Zhang,Yanxin Lei. The solvability of some kinds of singular integral equations of convolution type with variable integral limits[J]. Journal of Applied Analysis & Computation, 2024, 14(4) |
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| 作者姓名： | Pingrun Li Wenwen Zhang Yanxin Lei |
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| 摘 要： |
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| 收稿时间： | 2023-09-24 |
| 修稿时间： | 2024-01-20 |
The solvability of some kinds of singular integral equations of convolution type with variable integral limits |
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| Affiliation: | School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China,School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China,School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China |
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| Abstract: | 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. |
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| Keywords: | Singular integral equations variable integral limits Riemann boundary value problems Wiener-Hopf type dual type Fourier integral transform |
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