SOLVABILITY OF A CLASS OF CONVOLUTION INTEGRAL EQUATIONS WITH SINGULAR INTEGRAL–DIFFERENTIAL OPERATORS

Mincheng Wang; Pingrun Li

doi:10.11948/20240485

2025 Volume 15 Issue 4

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Mincheng Wang, Pingrun Li. SOLVABILITY OF A CLASS OF CONVOLUTION INTEGRAL EQUATIONS WITH SINGULAR INTEGRAL–DIFFERENTIAL OPERATORS[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 2408-2426. doi: 10.11948/20240485

Citation:

Mincheng Wang, Pingrun Li. SOLVABILITY OF A CLASS OF CONVOLUTION INTEGRAL EQUATIONS WITH SINGULAR INTEGRAL–DIFFERENTIAL OPERATORS[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 2408-2426. doi: 10.11948/20240485

SOLVABILITY OF A CLASS OF CONVOLUTION INTEGRAL EQUATIONS WITH SINGULAR INTEGRAL–DIFFERENTIAL OPERATORS

Mincheng Wang^1,,
Pingrun Li^2, ,

1.
Department of Mathematics, The Chinese University of Hong Kong, Hong Kong 999077, China
2.
School of Mathematical Science, Qufu Normal University, Qufu 273165, China

Author Bio: Email: Megan@link.cuhk.edu.hk(M. Wang)
Corresponding author: Email: lipingrun@163.com(P. Li)

Abstract

Abstract

In this paper, we consider a class of convolution integral equations with singular integral-differential operators. First, we establish the relation between Fourier analysis theory and Riemann boundary value problems, and investigate the theory of Noether solvability and some properties of Cauchy integral operators. Via using Fourier transform, we convert such equations into complex boundary value problems. By means of the regularity theory of the classical Riemann-Hilbert problems and of the theory of complex analysis, we obtain the conditions of Noether solvability and analytical solutions. In addition, we also study the analytical property of solution near nodes. Thus, this article is significant for the study of developing complex analysis, functional analysis, integral equations and complex boundary value problems, and it also provides theoretical support to quantum field theory and Ising model.
- Convolution integral equations /
- Riemann-Hilbert problems /
- singular integral-differential operators /
- Noether theory /
- Fourier transform
MSC: 45E10, 45E05, 47G20, 30E25

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References

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