A NEW EFFICIENT METHOD FOR TWO CLASSES OF SINGULAR CONVOLUTION INTEGRAL EQUATIONS OF NON-NORMAL TYPE WITH CAUCHY KERNEL

Meng Sun; Pingrun Li; Songwei Bai

doi:10.11948/20220165

2022 Volume 12 Issue 5

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Meng Sun, Pingrun Li, Songwei Bai. A NEW EFFICIENT METHOD FOR TWO CLASSES OF SINGULAR CONVOLUTION INTEGRAL EQUATIONS OF NON-NORMAL TYPE WITH CAUCHY KERNEL[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 2057-2074. doi: 10.11948/20220165

Citation:

Meng Sun, Pingrun Li, Songwei Bai. A NEW EFFICIENT METHOD FOR TWO CLASSES OF SINGULAR CONVOLUTION INTEGRAL EQUATIONS OF NON-NORMAL TYPE WITH CAUCHY KERNEL[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 2057-2074. doi: 10.11948/20220165

A NEW EFFICIENT METHOD FOR TWO CLASSES OF SINGULAR CONVOLUTION INTEGRAL EQUATIONS OF NON-NORMAL TYPE WITH CAUCHY KERNEL

1.
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Corresponding author: Email address: lipingrun@163.com(P. Li)

Abstract

Abstract

In this article, our task is to study the existence and Noethericity of solution for two classes of singular convolution integral equations with Cauchy kernels in the non-normal type case. To obtain the conditions of solvability for such equations, we establish regularity theory of solvability. By means of the theory of Fourier analysis, we will transform the equations into boundary value problems for holomorphic functions. The holomorphic solutions and conditions of solvability are obtained by using the method of complex analysis in class {0}. Moreover, we also discuss the asymptotic property of solution near nodes. Therefore, our work generalizes and improves the theories of integral equations and the classical boundary value problems for holomorphic functions.
- Singular convolution integral equations /
- boundary value problems for holomorphic functions /
- Wiener-Hopf equation /
- dual equations /
- Cauchy kernel /
- non-normal type
MSC: 45E10, 45E05, 30E25

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References

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